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	<title>Lösung von Aufgabe 4.3 P (WS 14/15) - Versionsgeschichte</title>
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	<updated>2026-08-14T04:56:09Z</updated>
	<subtitle>Versionsgeschichte dieser Seite in Geometrie-Wiki</subtitle>
	<generator>MediaWiki 1.43.9</generator>
	<entry>
		<id>http://geometrie.idea-sketch.com/index.php?title=L%C3%B6sung_von_Aufgabe_4.3_P_(WS_14/15)&amp;diff=27297&amp;oldid=prev</id>
		<title>EarlHickey am 9. Februar 2015 um 11:26 Uhr</title>
		<link rel="alternate" type="text/html" href="http://geometrie.idea-sketch.com/index.php?title=L%C3%B6sung_von_Aufgabe_4.3_P_(WS_14/15)&amp;diff=27297&amp;oldid=prev"/>
		<updated>2015-02-09T11:26:48Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;de&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Nächstältere Version&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Version vom 9. Februar 2015, 11:26 Uhr&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l7&quot;&gt;Zeile 7:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Zeile 7:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;zu a) M = {s.D., D, P, Ra, Re, Q}&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;zu a) M = {s.D., D, P, Ra, Re, Q}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;  die schiefen Drachen müssen hier nicht mit rein genommen werden --[[Benutzer:Schnirch|Schnirch]] ([[Benutzer Diskussion:Schnirch|Diskussion]]) 14:22, 19. Nov. 2014 (CET)&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;  die schiefen Drachen müssen hier nicht mit rein genommen werden --[[Benutzer:Schnirch|Schnirch]] ([[Benutzer Diskussion:Schnirch|Diskussion]]) 14:22, 19. Nov. 2014 (CET)&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Mit schiefen Drachen (plural) sind ja wohl sD, P und Re gemeint? --[[Benutzer:EarlHickey|EarlHickey]] ([[Benutzer Diskussion:EarlHickey|Diskussion]]) 12:26, 9. Feb. 2015 (CET)&amp;lt;br /&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;br /&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;zu b) M x M = { &amp;#039;&amp;#039;&amp;#039;(D,D)&amp;#039;&amp;#039;&amp;#039;, (D,Ra), (D,Q), &amp;#039;&amp;#039;&amp;#039;(Ra,D), (Ra,Ra)&amp;#039;&amp;#039;&amp;#039;, (Ra,Q), &amp;#039;&amp;#039;&amp;#039;(Q,D), (Q,Ra), (Q,Q)&amp;#039;&amp;#039;&amp;#039;}&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;zu b) M x M = { &amp;#039;&amp;#039;&amp;#039;(D,D)&amp;#039;&amp;#039;&amp;#039;, (D,Ra), (D,Q), &amp;#039;&amp;#039;&amp;#039;(Ra,D), (Ra,Ra)&amp;#039;&amp;#039;&amp;#039;, (Ra,Q), &amp;#039;&amp;#039;&amp;#039;(Q,D), (Q,Ra), (Q,Q)&amp;#039;&amp;#039;&amp;#039;}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;

&lt;!-- diff cache key geometrie:diff:1.41:old-27104:rev-27297:php=table --&gt;
&lt;/table&gt;</summary>
		<author><name>EarlHickey</name></author>
	</entry>
	<entry>
		<id>http://geometrie.idea-sketch.com/index.php?title=L%C3%B6sung_von_Aufgabe_4.3_P_(WS_14/15)&amp;diff=27104&amp;oldid=prev</id>
		<title>Bienes am 21. November 2014 um 12:12 Uhr</title>
		<link rel="alternate" type="text/html" href="http://geometrie.idea-sketch.com/index.php?title=L%C3%B6sung_von_Aufgabe_4.3_P_(WS_14/15)&amp;diff=27104&amp;oldid=prev"/>
		<updated>2014-11-21T12:12:40Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;de&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Nächstältere Version&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Version vom 21. November 2014, 12:12 Uhr&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l7&quot;&gt;Zeile 7:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Zeile 7:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;zu a) M = {s.D., D, P, Ra, Re, Q}&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;zu a) M = {s.D., D, P, Ra, Re, Q}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;  die schiefen Drachen müssen hier nicht mit rein genommen werden --[[Benutzer:Schnirch|Schnirch]] ([[Benutzer Diskussion:Schnirch|Diskussion]]) 14:22, 19. Nov. 2014 (CET)&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;  die schiefen Drachen müssen hier nicht mit rein genommen werden --[[Benutzer:Schnirch|Schnirch]] ([[Benutzer Diskussion:Schnirch|Diskussion]]) 14:22, 19. Nov. 2014 (CET)&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;zu b) M x M = {&#039;&#039;&#039;(&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;s.&lt;/del&gt;D&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;.&lt;/del&gt;,&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;s.&lt;/del&gt;D&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;.&lt;/del&gt;)&#039;&#039;&#039;, (&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;s.&lt;/del&gt;D&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;.,D), (s.D.,P), (s.D.&lt;/del&gt;,Ra)&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, (s.D.,Re), (s.D.,Q), &#039;&#039;&#039;(D,s.D.), (D,D)&#039;&#039;&#039;&lt;/del&gt;, (D&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;,P), (D,Ra), (D,Re), (D,Q), &#039;&#039;&#039;(P,s.D.)&#039;&#039;&#039;, (P,D), &#039;&#039;&#039;(P,P)&#039;&#039;&#039;, (P,Ra), (P,Re), (P&lt;/del&gt;,Q), &#039;&#039;&#039;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;(Ra,s.D.), &lt;/del&gt;(Ra,D&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;), (Ra,P&lt;/del&gt;), (Ra,Ra)&#039;&#039;&#039;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, (Ra,Re)&lt;/del&gt;, (Ra,Q&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;),&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;zu b) M x M = { &#039;&#039;&#039;(D,D)&#039;&#039;&#039;, (D,Ra), (D,Q), &#039;&#039;&#039;(Ra,D), (Ra,Ra)&#039;&#039;&#039;, (Ra,Q), &#039;&#039;&#039;(Q,D), (Q,Ra), (Q,Q)&#039;&#039;&#039;}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;&#039;(Re,s.D.)&#039;&#039;&#039;, (Re,D&lt;/del&gt;), &#039;&#039;&#039;(&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Re,P)&#039;&#039;&#039;, (Re,Ra), &#039;&#039;&#039;(Re,Re)&#039;&#039;&#039;, (Re,&lt;/del&gt;Q&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;)&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;&#039;(Q,s.&lt;/del&gt;D&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;.), (Q,D), (Q,P&lt;/del&gt;), (Q,Ra&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;), (Q,Re&lt;/del&gt;), (Q,Q)&#039;&#039;&#039;}&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;zu c) Die Relation R angewendet auf M x M, habe ich in Aufgabe b) dick markiert.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;zu c) Die Relation R angewendet auf M x M, habe ich in Aufgabe b) dick markiert.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;zu d) Die Relation ist reflexiv und transitiv, aber nicht symmetrisch (z.B.: &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Re &lt;/del&gt;ist Teilmenge von &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;P&lt;/del&gt;, aber &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;P &lt;/del&gt;nicht Teilmenge von &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Re&lt;/del&gt;).&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;zu d) Die Relation ist reflexiv und transitiv, aber nicht symmetrisch (z.B.: &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Ra &lt;/ins&gt;ist Teilmenge von &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;D&lt;/ins&gt;, aber &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;D &lt;/ins&gt;nicht Teilmenge von &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Ra&lt;/ins&gt;).&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;--[[Benutzer:Bienes|Bienes]] ([[Benutzer Diskussion:Bienes|Diskussion]]) 13:12, 21. Nov. 2014 (CET)&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Bienes</name></author>
	</entry>
	<entry>
		<id>http://geometrie.idea-sketch.com/index.php?title=L%C3%B6sung_von_Aufgabe_4.3_P_(WS_14/15)&amp;diff=27094&amp;oldid=prev</id>
		<title>Schnirch am 19. November 2014 um 13:22 Uhr</title>
		<link rel="alternate" type="text/html" href="http://geometrie.idea-sketch.com/index.php?title=L%C3%B6sung_von_Aufgabe_4.3_P_(WS_14/15)&amp;diff=27094&amp;oldid=prev"/>
		<updated>2014-11-19T13:22:50Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;de&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Nächstältere Version&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Version vom 19. November 2014, 13:22 Uhr&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l6&quot;&gt;Zeile 6:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Zeile 6:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Einführung_P]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Einführung_P]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;zu a) M = {s.D., D, P, Ra, Re, Q}&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;zu a) M = {s.D., D, P, Ra, Re, Q}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; die schiefen Drachen müssen hier nicht mit rein genommen werden --[[Benutzer:Schnirch|Schnirch]] ([[Benutzer Diskussion:Schnirch|Diskussion]]) 14:22, 19. Nov. 2014 (CET)&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;zu b) M x M = {&amp;#039;&amp;#039;&amp;#039;(s.D.,s.D.)&amp;#039;&amp;#039;&amp;#039;, (s.D.,D), (s.D.,P), (s.D.,Ra), (s.D.,Re), (s.D.,Q), &amp;#039;&amp;#039;&amp;#039;(D,s.D.), (D,D)&amp;#039;&amp;#039;&amp;#039;, (D,P), (D,Ra), (D,Re), (D,Q), &amp;#039;&amp;#039;&amp;#039;(P,s.D.)&amp;#039;&amp;#039;&amp;#039;, (P,D), &amp;#039;&amp;#039;&amp;#039;(P,P)&amp;#039;&amp;#039;&amp;#039;, (P,Ra), (P,Re), (P,Q), &amp;#039;&amp;#039;&amp;#039;(Ra,s.D.), (Ra,D), (Ra,P), (Ra,Ra)&amp;#039;&amp;#039;&amp;#039;, (Ra,Re), (Ra,Q),&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;zu b) M x M = {&amp;#039;&amp;#039;&amp;#039;(s.D.,s.D.)&amp;#039;&amp;#039;&amp;#039;, (s.D.,D), (s.D.,P), (s.D.,Ra), (s.D.,Re), (s.D.,Q), &amp;#039;&amp;#039;&amp;#039;(D,s.D.), (D,D)&amp;#039;&amp;#039;&amp;#039;, (D,P), (D,Ra), (D,Re), (D,Q), &amp;#039;&amp;#039;&amp;#039;(P,s.D.)&amp;#039;&amp;#039;&amp;#039;, (P,D), &amp;#039;&amp;#039;&amp;#039;(P,P)&amp;#039;&amp;#039;&amp;#039;, (P,Ra), (P,Re), (P,Q), &amp;#039;&amp;#039;&amp;#039;(Ra,s.D.), (Ra,D), (Ra,P), (Ra,Ra)&amp;#039;&amp;#039;&amp;#039;, (Ra,Re), (Ra,Q),&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;(Re,s.D.)&amp;#039;&amp;#039;&amp;#039;, (Re,D), &amp;#039;&amp;#039;&amp;#039;(Re,P)&amp;#039;&amp;#039;&amp;#039;, (Re,Ra), &amp;#039;&amp;#039;&amp;#039;(Re,Re)&amp;#039;&amp;#039;&amp;#039;, (Re,Q), &amp;#039;&amp;#039;&amp;#039;(Q,s.D.), (Q,D), (Q,P), (Q,Ra), (Q,Re), (Q,Q)&amp;#039;&amp;#039;&amp;#039;}&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;(Re,s.D.)&amp;#039;&amp;#039;&amp;#039;, (Re,D), &amp;#039;&amp;#039;&amp;#039;(Re,P)&amp;#039;&amp;#039;&amp;#039;, (Re,Ra), &amp;#039;&amp;#039;&amp;#039;(Re,Re)&amp;#039;&amp;#039;&amp;#039;, (Re,Q), &amp;#039;&amp;#039;&amp;#039;(Q,s.D.), (Q,D), (Q,P), (Q,Ra), (Q,Re), (Q,Q)&amp;#039;&amp;#039;&amp;#039;}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Schnirch</name></author>
	</entry>
	<entry>
		<id>http://geometrie.idea-sketch.com/index.php?title=L%C3%B6sung_von_Aufgabe_4.3_P_(WS_14/15)&amp;diff=27080&amp;oldid=prev</id>
		<title>Bienes am 16. November 2014 um 12:43 Uhr</title>
		<link rel="alternate" type="text/html" href="http://geometrie.idea-sketch.com/index.php?title=L%C3%B6sung_von_Aufgabe_4.3_P_(WS_14/15)&amp;diff=27080&amp;oldid=prev"/>
		<updated>2014-11-16T12:43:01Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;de&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Nächstältere Version&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Version vom 16. November 2014, 12:43 Uhr&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l5&quot;&gt;Zeile 5:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Zeile 5:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Einführung_P]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Einführung_P]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;zu a) M = {s.D., D, P, Ra, Re, Q}&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;zu b) M x M = {&#039;&#039;&#039;(s.D.,s.D.)&#039;&#039;&#039;, (s.D.,D), (s.D.,P), (s.D.,Ra), (s.D.,Re), (s.D.,Q), &#039;&#039;&#039;(D,s.D.), (D,D)&#039;&#039;&#039;, (D,P), (D,Ra), (D,Re), (D,Q), &#039;&#039;&#039;(P,s.D.)&#039;&#039;&#039;, (P,D), &#039;&#039;&#039;(P,P)&#039;&#039;&#039;, (P,Ra), (P,Re), (P,Q), &#039;&#039;&#039;(Ra,s.D.), (Ra,D), (Ra,P), (Ra,Ra)&#039;&#039;&#039;, (Ra,Re), (Ra,Q),&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;&#039;(Re,s.D.)&#039;&#039;&#039;, (Re,D), &#039;&#039;&#039;(Re,P)&#039;&#039;&#039;, (Re,Ra), &#039;&#039;&#039;(Re,Re)&#039;&#039;&#039;, (Re,Q), &#039;&#039;&#039;(Q,s.D.), (Q,D), (Q,P), (Q,Ra), (Q,Re), (Q,Q)&#039;&#039;&#039;}&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;zu c) Die Relation R angewendet auf M x M, habe ich in Aufgabe b) dick markiert.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;zu d) Die Relation ist reflexiv und transitiv, aber nicht symmetrisch (z.B.: Re ist Teilmenge von P, aber P nicht Teilmenge von Re).&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;

&lt;!-- diff cache key geometrie:diff:1.41:old-27038:rev-27080:php=table --&gt;
&lt;/table&gt;</summary>
		<author><name>Bienes</name></author>
	</entry>
	<entry>
		<id>http://geometrie.idea-sketch.com/index.php?title=L%C3%B6sung_von_Aufgabe_4.3_P_(WS_14/15)&amp;diff=27038&amp;oldid=prev</id>
		<title>Schnirch: Die Seite wurde neu angelegt: „a) Geben Sie die Menge &lt;math&gt;M&lt;/math&gt; aller konvexer Drachenvierecke an.&lt;br /&gt; b) Bilden Sie das kartesische Produkt der Menge &lt;math&gt;M \times M&lt;/math&gt;.&lt;br /&gt; c…“</title>
		<link rel="alternate" type="text/html" href="http://geometrie.idea-sketch.com/index.php?title=L%C3%B6sung_von_Aufgabe_4.3_P_(WS_14/15)&amp;diff=27038&amp;oldid=prev"/>
		<updated>2014-11-11T12:19:19Z</updated>

		<summary type="html">&lt;p&gt;Die Seite wurde neu angelegt: „a) Geben Sie die Menge &amp;lt;math&amp;gt;M&amp;lt;/math&amp;gt; aller konvexer Drachenvierecke an.&amp;lt;br /&amp;gt; b) Bilden Sie das kartesische Produkt der Menge &amp;lt;math&amp;gt;M \times M&amp;lt;/math&amp;gt;.&amp;lt;br /&amp;gt; c…“&lt;/p&gt;
&lt;p&gt;&lt;b&gt;Neue Seite&lt;/b&gt;&lt;/p&gt;&lt;div&gt;a) Geben Sie die Menge &amp;lt;math&amp;gt;M&amp;lt;/math&amp;gt; aller konvexer Drachenvierecke an.&amp;lt;br /&amp;gt;&lt;br /&gt;
b) Bilden Sie das kartesische Produkt der Menge &amp;lt;math&amp;gt;M \times M&amp;lt;/math&amp;gt;.&amp;lt;br /&amp;gt;&lt;br /&gt;
c) Wir definineren eine Relation &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; mit &amp;lt;math&amp;gt;R:=A\subseteq B&amp;lt;/math&amp;gt;. Bestimmen Sie die Relation &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; auf &amp;lt;math&amp;gt;M \times M&amp;lt;/math&amp;gt;.&amp;lt;br /&amp;gt;&lt;br /&gt;
d) Untersuchen Sie die Relation &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; auf ihre Eigenschaften (reflexiv, symmetrisch, transitiv).&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Category:Einführung_P]]&lt;/div&gt;</summary>
		<author><name>Schnirch</name></author>
	</entry>
</feed>