MAT 243 1.3 Propositional Equivalence

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Key Equivalences

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13 Terms

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Definition of the Conditional

p→q≡¬p∨q

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The Laws of De Morgan

¬(p∧q)≡¬p∨¬q
¬(p∨q)≡¬p∧¬q

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Negation of Conditionals

¬(p→q)≡¬(¬p∨q)≡p∧¬q

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Commutative Laws

p∨q≡q∨p
p∧q≡q∧p

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Associative Laws

p∨(q∨r)≡(p∨q)∨r
p∧(q∧r)≡(p∧q)∧r

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Distributive Laws

p∨(q∧r)≡(p∨q)∧(p∨r)
p∧(q∨r)≡(p∧q)∨(p∧r)

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Identity Laws

p∨F≡p
p∧T≡p

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Domination Laws

p∨T≡T
p∧F≡F

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Idempotent Laws

p∨p≡p
p∧p≡p

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Double Negation Law

¬(¬p)≡p

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Absorption Laws

p∨(p∧q)≡p
p∧(p∨q)≡p

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Conditional ≡ Contrapositive

p→q≡¬q→¬p

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Inverse ≡ Converse

q→p≡¬p→¬q