Logic/De Morgan's laws

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(Created page with 'Logic > De Morgan's laws == Contents == * Category:Mathematical logic（Wikipedia） * [[wikipedia:Boolean_algebra_(logic)|Boole…')
 
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* [[wikipedia:Boolean_algebra_(logic)|Boolean algebra (logic)]]
* [[wikipedia:Boolean_algebra_(logic)|Boolean algebra (logic)]]
* [[wikipedia:De_Morgan%27s_laws|De_Morgan's laws]]
* [[wikipedia:De_Morgan%27s_laws|De_Morgan's laws]]
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== Overview ==
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=== Definition of De Morgan's laws by truth table ===
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0 means false, 1 means true, and ≡ means equivalent.
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Case of "￢(P∧Q)" ≡ "￢P∨￢Q".
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{| border="1" class="wikitable" style="background-color:#ddf"
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! style="background:#ffdead;" |　P　
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! style="background:#ffdead;" |　Q　
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! style="background:#ffdead;" |　P∧Q　
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! style="background:#ffdead;" |　￢P　
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! style="background:#ffdead;" |　￢Q　
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! style="background:#ffdead;" |　￢P∨￢Q　
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! style="background:#ffdead;" |　￢（P∧Q）　
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|-
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|　0
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|　0
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|　0
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|　1
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|　1
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|　1
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|　1
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|-
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|　0
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|　1
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|　0
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|　1
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|　0
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|　1
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|　1
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|-
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|　1
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|　0
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|　0
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|　0
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|　1
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|　1
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|　1
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|-
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|　1
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|　1
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|　1
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|　0
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|　0
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|　0
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|　0
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|-
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|}
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Case of "￢(P∨Q)" ≡ "￢P∧￢Q".
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{| border="1" class="wikitable" style="background-color:#ddf"
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! style="background:#ffdead;" |　P　
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! style="background:#ffdead;" |　Q　
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! style="background:#ffdead;" |　P∨Q　
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! style="background:#ffdead;" |　￢P　
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! style="background:#ffdead;" |　￢Q　
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! style="background:#ffdead;" |　￢P∧￢Q　
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! style="background:#ffdead;" |　￢（P∨Q）　
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|-
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|　0
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|　0
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|　0
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|　1
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|　1
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|　1
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|　1
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|-
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|　0
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|　1
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|　1
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|　1
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|　0
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|　0
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|　0
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|-
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|　1
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|　0
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|　1
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|　0
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|　1
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|　0
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|　0
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|-
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|　1
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|　1
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|　1
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|　0
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|　0
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|　0
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|　0
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|-
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|}
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== CAI Exercise ==
== CAI Exercise ==

Latest revision as of 08:32, 23 May 2014

Logic > De Morgan's laws

Contents

Contents

Overview

Definition of De Morgan's laws by truth table

0 means false, 1 means true, and ≡ means equivalent.

Case of "￢(P∧Q)" ≡ "￢P∨￢Q".

　P　 　Q　 　P∧Q　 　￢P　 　￢Q　 　￢P∨￢Q　 　￢（P∧Q）　
　0 　0 　0 　1 　1 　1 　1
　0 　1 　0 　1 　0 　1 　1
　1 　0 　0 　0 　1 　1 　1
　1 　1 　1 　0 　0 　0 　0

Case of "￢(P∨Q)" ≡ "￢P∧￢Q".

　P　 　Q　 　P∨Q　 　￢P　 　￢Q　 　￢P∧￢Q　 　￢（P∨Q）　
　0 　0 　0 　1 　1 　1 　1
　0 　1 　1 　1 　0 　0 　0
　1 　0 　1 　0 　1 　0 　0
　1 　1 　1 　0 　0 　0 　0


CAI Exercise

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