Logical Equivalence
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Commutative laws: p Ù q = q Ù p, p Ú q = q Ú p
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Associative laws: (p Ù q) Ù r = p Ù (q Ù r), (p Ú q) Ú r = p Ú (q Ú r)
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Distributive laws: p Ù
(q Ú r) = (p Ù q) Ú (p Ù r)
p
Ú (q Ù r) = (p Ú q) Ù (p Ú r)
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Identity laws: p Ù t = p, p Ú c = p
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Negation laws: p Ú ~p = t, p Ù ~p = c
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Double negative law: ~(~p)
= p
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Idempotent laws: p Ù p = p, p Ú p = p
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De Morgan’s laws: ~(p Ù q) = ~p Ú ~q, ~(p Ú q) = ~p Ù ~q
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Universal bound laws: p Ú t = t, p Ù c = c
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Absorption laws: p Ú (p Ù q) = p, p Ù (p Ú q) = p
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Negation of t and c: ~t =
c, ~c = t
