File:Venn 0000 0000 0000 0001.png

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Original file ‎(1,024 × 1,024 pixels, file size: 130 KB, MIME type: image/png)

Summary

The 15 cells of these Venn diagrams (except the surrounding) correspond to the vertices of the tesseracts tetrahedral shadow.

This is a 4 shphere Venn diagram, representing a 4-ary Boolean function.


The spheres Venn 0101 0101 0101 0101.pngVenn 0011 0011 0011 0011.pngVenn 0000 1111 0000 1111.pngVenn 0000 0000 1111 1111.png stand for sets or statements A, B, C, D.


Examples:


A \cap B \cap C~     =~     A \cap B \cap C
Venn 0001 0001 0001 0001.png \cap Venn 0000 1111 0000 1111.png     =~     Venn 0000 0001 0000 0001.png


A \cap B \cap C \cap D~     =~     A \cap B \cap C \cap D
Venn 0000 0001 0000 0001.png \cap Venn 0000 0000 1111 1111.png     =~     Venn 0000 0000 0000 0001.png


\{ \}^C~ \setminus~ D~     =~     D^C~
Venn 1111 1111 1111 1111.png \setminus~ Venn 0000 0000 1111 1111.png     =~     Venn 1111 1111 0000 0000.png


The POV-Ray source is given for File:Venn 0000 0001 0001 0110.png and File:Venn 1111 1111 0000 0000.png.

Copyright status:

GNU Free Documentation License, Version 1.2

Source:

https://commons.wikimedia.org/wiki/User:Watchduck

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current02:11, 13 January 2017Thumbnail for version as of 02:11, 13 January 20171,024 × 1,024 (130 KB)127.0.0.1 (talk)<p>This is a 4 shphere <a href="https://en.wikipedia.org/wiki/Venn_diagram" class="extiw" title="w:Venn diagram">Venn diagram</a>, representing a 4-<a href="https://en.wikipedia.org/wiki/Arity" class="extiw" title="w:Arity">ary</a> <a href="https://en.wikipedia.org/wiki/Boolean_function" class="extiw" title="w:Boolean function">Boolean function</a>. </p> <p><br> The spheres <a href="//commons.wikimedia.org/wiki/File:Venn_0101_0101_0101_0101.png" class="image"><img alt="Venn 0101 0101 0101 0101.png" src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Venn_0101_0101_0101_0101.png/80px-Venn_0101_0101_0101_0101.png" width="80" height="80" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Venn_0101_0101_0101_0101.png/120px-Venn_0101_0101_0101_0101.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Venn_0101_0101_0101_0101.png/160px-Venn_0101_0101_0101_0101.png 2x" data-file-width="1024" data-file-height="1024"></a><a href="//commons.wikimedia.org/wiki/File:Venn_0011_0011_0011_0011.png" class="image"><img alt="Venn 0011 0011 0011 0011.png" src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Venn_0011_0011_0011_0011.png/80px-Venn_0011_0011_0011_0011.png" width="80" height="80" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Venn_0011_0011_0011_0011.png/120px-Venn_0011_0011_0011_0011.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Venn_0011_0011_0011_0011.png/160px-Venn_0011_0011_0011_0011.png 2x" data-file-width="1024" data-file-height="1024"></a><a href="//commons.wikimedia.org/wiki/File:Venn_0000_1111_0000_1111.png" class="image"><img alt="Venn 0000 1111 0000 1111.png" src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Venn_0000_1111_0000_1111.png/80px-Venn_0000_1111_0000_1111.png" width="80" height="80" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Venn_0000_1111_0000_1111.png/120px-Venn_0000_1111_0000_1111.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Venn_0000_1111_0000_1111.png/160px-Venn_0000_1111_0000_1111.png 2x" data-file-width="1024" data-file-height="1024"></a><a href="//commons.wikimedia.org/wiki/File:Venn_0000_0000_1111_1111.png" class="image"><img alt="Venn 0000 0000 1111 1111.png" src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/51/Venn_0000_0000_1111_1111.png/80px-Venn_0000_0000_1111_1111.png" width="80" height="80" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/5/51/Venn_0000_0000_1111_1111.png/120px-Venn_0000_0000_1111_1111.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/5/51/Venn_0000_0000_1111_1111.png/160px-Venn_0000_0000_1111_1111.png 2x" data-file-width="1024" data-file-height="1024"></a> stand for sets or statements A, B, C, D. </p> <p><br> Examples: </p> <p><br></p> <table style="text-align: center; border: 1px solid darkgray; width:400px"> <tr> <td> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>A</mi><mo>∩<!-- ∩ --></mo><mi>B</mi></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle A\cap B}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb27b38cf9eac6060e67b61f66cd9beec5067f81" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:6.121ex; height:2.343ex;" alt="A\cap B"></span> </td> <td> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>∩<!-- ∩ --></mo></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \cap }</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d4e886e6f5a28a33e073fb108440c152ecfe2d3" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:1.561ex; height:2.009ex;" alt="\cap "></span> </td> <td> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>C</mi><mtext> </mtext></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle C~}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6e137859d9f479134e5dcf883181baab50a2640" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:2.357ex; height:2.176ex;" alt="C~"></span> </td> <td>    <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>=</mo><mtext> </mtext></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle =~}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2367ce4d9084457c631913997649869fabbc36be" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.171ex; width:3.044ex; height:1.343ex;" alt="=~"></span>     </td> <td> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>A</mi><mo>∩<!-- ∩ --></mo><mi>B</mi><mo>∩<!-- ∩ --></mo><mi>C</mi></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle A\cap B\cap C}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24cedf001cf394b59a4cb1a939ab567910dfb415" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:10.491ex; height:2.343ex;" alt="A\cap B\cap C"></span> </td> </tr> <tr> <td> <a href="//commons.wikimedia.org/wiki/File:Venn_0001_0001_0001_0001.png" class="image"><img alt="Venn 0001 0001 0001 0001.png" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/77/Venn_0001_0001_0001_0001.png/100px-Venn_0001_0001_0001_0001.png" width="100" height="100" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/7/77/Venn_0001_0001_0001_0001.png/150px-Venn_0001_0001_0001_0001.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/7/77/Venn_0001_0001_0001_0001.png/200px-Venn_0001_0001_0001_0001.png 2x" data-file-width="1024" data-file-height="1024"></a> </td> <td> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>∩<!-- ∩ --></mo></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \cap }</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d4e886e6f5a28a33e073fb108440c152ecfe2d3" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:1.561ex; height:2.009ex;" alt="\cap "></span> </td> <td> <a href="//commons.wikimedia.org/wiki/File:Venn_0000_1111_0000_1111.png" class="image"><img alt="Venn 0000 1111 0000 1111.png" src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Venn_0000_1111_0000_1111.png/100px-Venn_0000_1111_0000_1111.png" width="100" height="100" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Venn_0000_1111_0000_1111.png/150px-Venn_0000_1111_0000_1111.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Venn_0000_1111_0000_1111.png/200px-Venn_0000_1111_0000_1111.png 2x" data-file-width="1024" data-file-height="1024"></a> </td> <td>    <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>=</mo><mtext> </mtext></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle =~}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2367ce4d9084457c631913997649869fabbc36be" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.171ex; width:3.044ex; height:1.343ex;" alt="=~"></span>     </td> <td> <a href="//commons.wikimedia.org/wiki/File:Venn_0000_0001_0000_0001.png" class="image"><img alt="Venn 0000 0001 0000 0001.png" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Venn_0000_0001_0000_0001.png/100px-Venn_0000_0001_0000_0001.png" width="100" height="100" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Venn_0000_0001_0000_0001.png/150px-Venn_0000_0001_0000_0001.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Venn_0000_0001_0000_0001.png/200px-Venn_0000_0001_0000_0001.png 2x" data-file-width="1024" data-file-height="1024"></a> </td> </tr> </table> <p><br></p> <table style="text-align: center; border: 1px solid darkgray; width:400px"> <tr> <td> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>A</mi><mo>∩<!-- ∩ --></mo><mi>B</mi><mo>∩<!-- ∩ --></mo><mi>C</mi></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle A\cap B\cap C}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24cedf001cf394b59a4cb1a939ab567910dfb415" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:10.491ex; height:2.343ex;" alt="A\cap B\cap C"></span> </td> <td> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>∩<!-- ∩ --></mo></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \cap }</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d4e886e6f5a28a33e073fb108440c152ecfe2d3" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:1.561ex; height:2.009ex;" alt="\cap "></span> </td> <td> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>D</mi><mtext> </mtext></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle D~}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/220a67d4e2b0aba95ad9be501231d1f9ff3799d3" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:2.515ex; height:2.176ex;" alt="D~"></span> </td> <td>    <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>=</mo><mtext> </mtext></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle =~}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2367ce4d9084457c631913997649869fabbc36be" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.171ex; width:3.044ex; height:1.343ex;" alt="=~"></span>     </td> <td> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>A</mi><mo>∩<!-- ∩ --></mo><mi>B</mi><mo>∩<!-- ∩ --></mo><mi>C</mi><mo>∩<!-- ∩ --></mo><mi>D</mi></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle A\cap B\cap C\cap D}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8f8614517bafcf29616cad632e05426ef848e76" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:15.019ex; height:2.343ex;" alt="A\cap B\cap C\cap D"></span> </td> </tr> <tr> <td> <a href="//commons.wikimedia.org/wiki/File:Venn_0000_0001_0000_0001.png" class="image"><img alt="Venn 0000 0001 0000 0001.png" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Venn_0000_0001_0000_0001.png/100px-Venn_0000_0001_0000_0001.png" width="100" height="100" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Venn_0000_0001_0000_0001.png/150px-Venn_0000_0001_0000_0001.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Venn_0000_0001_0000_0001.png/200px-Venn_0000_0001_0000_0001.png 2x" data-file-width="1024" data-file-height="1024"></a> </td> <td> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>∩<!-- ∩ --></mo></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \cap }</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d4e886e6f5a28a33e073fb108440c152ecfe2d3" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:1.561ex; height:2.009ex;" alt="\cap "></span> </td> <td> <a href="//commons.wikimedia.org/wiki/File:Venn_0000_0000_1111_1111.png" class="image"><img alt="Venn 0000 0000 1111 1111.png" src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/51/Venn_0000_0000_1111_1111.png/100px-Venn_0000_0000_1111_1111.png" width="100" height="100" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/5/51/Venn_0000_0000_1111_1111.png/150px-Venn_0000_0000_1111_1111.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/5/51/Venn_0000_0000_1111_1111.png/200px-Venn_0000_0000_1111_1111.png 2x" data-file-width="1024" data-file-height="1024"></a> </td> <td>    <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>=</mo><mtext> </mtext></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle =~}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2367ce4d9084457c631913997649869fabbc36be" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.171ex; width:3.044ex; height:1.343ex;" alt="=~"></span>     </td> <td> <a href="//commons.wikimedia.org/wiki/File:Venn_0000_0000_0000_0001.png" class="image"><img alt="Venn 0000 0000 0000 0001.png" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Venn_0000_0000_0000_0001.png/100px-Venn_0000_0000_0000_0001.png" width="100" height="100" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Venn_0000_0000_0000_0001.png/150px-Venn_0000_0000_0000_0001.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Venn_0000_0000_0000_0001.png/200px-Venn_0000_0000_0000_0001.png 2x" data-file-width="1024" data-file-height="1024"></a> </td> </tr> </table> <p><br></p> <table style="text-align: center; border: 1px solid darkgray; width:400px"> <tr> <td> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo fence="false" stretchy="false">{</mo><msup><mo fence="false" stretchy="false">}</mo><mrow class="MJX-TeXAtom-ORD"><mi>C</mi></mrow></msup><mtext> </mtext></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \{\}^{C}~}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f67c68219c13151f4d4da1bf08c487f12cb64005" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.838ex; width:4.415ex; height:3.176ex;" alt="\{\}^{C}~"></span> </td> <td> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo class="MJX-variant">∖<!-- ∖ --></mo><mtext> </mtext></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \setminus ~}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ad5259e4d0c02e97dabe8a32a6ea1649287443d" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.838ex; width:1.754ex; height:2.843ex;" alt="\setminus ~"></span> </td> <td> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>D</mi><mtext> </mtext></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle D~}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/220a67d4e2b0aba95ad9be501231d1f9ff3799d3" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:2.515ex; height:2.176ex;" alt="D~"></span> </td> <td>    <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>=</mo><mtext> </mtext></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle =~}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2367ce4d9084457c631913997649869fabbc36be" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.171ex; width:3.044ex; height:1.343ex;" alt="=~"></span>     </td> <td> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>D</mi><mrow class="MJX-TeXAtom-ORD"><mi>C</mi></mrow></msup><mtext> </mtext></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle D^{C}~}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/500dd02c047b64d3f6b056524e4194910ddc1726" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:4.004ex; height:2.676ex;" alt="D^{C}~"></span> </td> </tr> <tr> <td> <a href="//commons.wikimedia.org/wiki/File:Venn_1111_1111_1111_1111.png" class="image"><img alt="Venn 1111 1111 1111 1111.png" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Venn_1111_1111_1111_1111.png/100px-Venn_1111_1111_1111_1111.png" width="100" height="100" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Venn_1111_1111_1111_1111.png/150px-Venn_1111_1111_1111_1111.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Venn_1111_1111_1111_1111.png/200px-Venn_1111_1111_1111_1111.png 2x" data-file-width="1024" data-file-height="1024"></a> </td> <td> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo class="MJX-variant">∖<!-- ∖ --></mo><mtext> </mtext></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \setminus ~}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ad5259e4d0c02e97dabe8a32a6ea1649287443d" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.838ex; width:1.754ex; height:2.843ex;" alt="\setminus ~"></span> </td> <td> <a href="//commons.wikimedia.org/wiki/File:Venn_0000_0000_1111_1111.png" class="image"><img alt="Venn 0000 0000 1111 1111.png" src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/51/Venn_0000_0000_1111_1111.png/100px-Venn_0000_0000_1111_1111.png" width="100" height="100" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/5/51/Venn_0000_0000_1111_1111.png/150px-Venn_0000_0000_1111_1111.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/5/51/Venn_0000_0000_1111_1111.png/200px-Venn_0000_0000_1111_1111.png 2x" data-file-width="1024" data-file-height="1024"></a> </td> <td>    <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>=</mo><mtext> </mtext></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle =~}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2367ce4d9084457c631913997649869fabbc36be" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.171ex; width:3.044ex; height:1.343ex;" alt="=~"></span>     </td> <td> <a href="//commons.wikimedia.org/wiki/File:Venn_1111_1111_0000_0000.png" class="image"><img alt="Venn 1111 1111 0000 0000.png" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Venn_1111_1111_0000_0000.png/100px-Venn_1111_1111_0000_0000.png" width="100" height="100" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Venn_1111_1111_0000_0000.png/150px-Venn_1111_1111_0000_0000.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Venn_1111_1111_0000_0000.png/200px-Venn_1111_1111_0000_0000.png 2x" data-file-width="1024" data-file-height="1024"></a> </td> </tr> </table> <p><br></p> <div class="thumb tleft"><div class="thumbinner" style="width:402px;"> <a href="//commons.wikimedia.org/wiki/File:Tesseract_tetrahedron_shadow_matrices.svg" class="image"><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/02/Tesseract_tetrahedron_shadow_matrices.svg/400px-Tesseract_tetrahedron_shadow_matrices.svg.png" width="400" height="526" class="thumbimage" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/0/02/Tesseract_tetrahedron_shadow_matrices.svg/600px-Tesseract_tetrahedron_shadow_matrices.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/0/02/Tesseract_tetrahedron_shadow_matrices.svg/800px-Tesseract_tetrahedron_shadow_matrices.svg.png 2x" data-file-width="730" data-file-height="960"></a> <div class="thumbcaption"> <div class="magnify"><a href="//commons.wikimedia.org/wiki/File:Tesseract_tetrahedron_shadow_matrices.svg" class="internal" title="Enlarge"></a></div>The 15 cells of these Venn diagrams (except the surrounding) correspond to the vertices of the <a href="https://en.wikipedia.org/wiki/Tesseract" class="extiw" title="w:Tesseract">tesseracts</a> <a href="https://en.wikipedia.org/wiki/Tetrahedron" class="extiw" title="w:Tetrahedron">tetrahedral</a> shadow.</div> </div></div> <p><br clear="all"><br><br><br><br> The POV-Ray source is given for <a href="//commons.wikimedia.org/wiki/File:Venn_0000_0001_0001_0110.png" title="File:Venn 0000 0001 0001 0110.png">File:Venn 0000 0001 0001 0110.png</a> and <a href="//commons.wikimedia.org/wiki/File:Venn_1111_1111_0000_0000.png" title="File:Venn 1111 1111 0000 0000.png">File:Venn 1111 1111 0000 0000.png</a>. </p> <div class="mw-content-ltr"> <table cellspacing="0" style="color:#000;background:#DDD;border:1px solid #BBB;margin:.1em;width:;" class="createdwithtemplate layouttemplate"><tr> <td style="width:1.2em;height:1.2em;padding:.2em;"> <div class="center"><div class="floatnone"><a href="//commons.wikimedia.org/wiki/File:Povray_logo_sphere.png" title="File:Povray logo sphere.png"><img alt="Povray logo sphere.png" src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/62/Povray_logo_sphere.png/20px-Povray_logo_sphere.png" width="20" height="20" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/6/62/Povray_logo_sphere.png/30px-Povray_logo_sphere.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/6/62/Povray_logo_sphere.png/40px-Povray_logo_sphere.png 2x" data-file-width="512" data-file-height="512"></a></div></div> </td> <td style="font-size:.85em;padding:.2em;vertical-align:middle;">This image was created with <a href="https://en.wikipedia.org/wiki/POV-Ray" class="extiw" title="en:POV-Ray">POV-Ray</a> </td> </tr></table> </div> <div class="mw-content-ltr"> <table cellspacing="0" style="color:#000;background:#DDD;border:1px solid #BBB;margin:.1em;width:;" class="createdwithtemplate layouttemplate"><tr> <td style="width:1.2em;height:1.2em;padding:.2em;"> <div class="center"><div class="floatnone"><a href="//commons.wikimedia.org/wiki/File:Commonist.svg" title="File:Commonist.svg"><img alt="Commonist.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Commonist.svg/20px-Commonist.svg.png" width="20" height="20" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Commonist.svg/30px-Commonist.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Commonist.svg/40px-Commonist.svg.png 2x" data-file-width="512" data-file-height="512"></a></div></div> </td> <td style="font-size:.85em;padding:.2em;vertical-align:middle;">This file was uploaded with <b><a href="//commons.wikimedia.org/wiki/Commonist" class="mw-redirect" title="Commonist">Commonist</a></b>. </td> </tr></table> </div>
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