Useful logical equivalences
Equivalence Name
p?T ? p Identity
p?F ? p laws
p?T ? T Domination
p?F ? F laws
p?p ? p Idempotent
p?p ? p laws
??p ?p Double
negation law
Equivalence Name
p?q ? q?p Commutative
p?q ? q?p laws
(p?q)?r ? p?(q?r) Associative
(p?q)?r ? p?(q?r) laws
p?(q?r) ? (p?q)?(p?r) Distributive
p?(q?r) ? (p?q)?(p?r) laws
?(p?q) ? ?p??q De Morgan’s
?(p?q) ? ?p??q laws
Below T denotes any tautolody and F denotes any contradiction
p??p ? T p??p ? F p?q ? ?p?q
1.2
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