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For example, consider the case where ''k'' = 3. Then the minimal negation operation <math>\nu (p, q, r)\!</math>, when there is no risk of confusion written more simply as <math>(p, q, r)\!</math>, has the following venn diagram:
For example, consider the case where ''k'' = 3. Then the minimal negation operation <math>\nu (p, q, r)\!</math>, when there is no risk of confusion written more simply as <math>(p, q, r)\!</math>, has the following venn diagram:
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<pre>
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{| align="center" cellpadding="10" style="text-align:center"
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o-------------------------------------------------o
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|
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<p>[[Image:Minimal_Negation_Operator_1.jpg|500px]]</p>
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<p><math>\text{Figure 1.}\quad (p, q, r)\!</math>
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| o-------------o |
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|}
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| / \ |
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| / \ |
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| / \ |
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| / \ |
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| o o |
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| | P | |
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| | | |
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| | | |
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| o---o---------o o---------o---o |
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| / \`````````\ /`````````/ \ |
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| / \`````````o`````````/ \ |
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| / \```````/ \```````/ \ |
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| / \`````/ \`````/ \ |
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| o o---o-----o---o o |
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| | |`````| | |
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| | |`````| | |
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| | Q |`````| R | |
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| o o`````o o |
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| \ \```/ / |
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| \ \`/ / |
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| \ o / |
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| \ / \ / |
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| o-------------o o-------------o |
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o-------------------------------------------------o
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Figure 1. (p, q, r)
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</pre>
For a contrasting example, the boolean function expressed by the form <math>((p),(q),(r))\!</math> has the following venn diagram:
For a contrasting example, the boolean function expressed by the form <math>((p),(q),(r))\!</math> has the following venn diagram:
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<pre>
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{| align="center" cellpadding="10" style="text-align:center"
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o-------------------------------------------------o
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<p>[[Image:Minimal_Negation_Operator_2.jpg|500px]]</p>
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<p><math>\text{Figure 2.}\quad ((p),(q),(r))\!</math>
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|}
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| /```````````````\ |
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| /`````````````````\ |
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| /```````````````````\ |
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| /`````````````````````\ |
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| o```````````````````````o |
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| |`````````` P ``````````| |
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| |```````````````````````| |
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| |```````````````````````| |
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| o---o---------o```o---------o---o |
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| /`````\ \`/ /`````\ |
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| /```````\ o /```````\ |
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| /`````````\ / \ /`````````\ |
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| /```````````\ / \ /```````````\ |
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| o`````````````o---o-----o---o`````````````o |
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| |`````````````````| |`````````````````| |
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| |`````````````````| |`````````````````| |
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| |``````` Q ```````| |``````` R ```````| |
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| o`````````````````o o`````````````````o |
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| \`````````````````\ /`````````````````/ |
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| \`````````````````\ /`````````````````/ |
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| \`````````````````o`````````````````/ |
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| \```````````````/ \```````````````/ |
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| o-------------o o-------------o |
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o-------------------------------------------------o
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Figure 2. ((p),(q),(r))
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</pre>
==Glossary of basic terms==
==Glossary of basic terms==