Truth table

Definition

$p$	$q$	$\neg p$	$p\vee q$	$p\wedge q$	$p\to q$	$p\leftrightarrow q$
T	T	F	T	T	T	T
T	F	F	F	T	F	F
F	T	T	F	T	T	F
F	F	T	F	F	T	T

Facts

$p\to q\equiv \neg p\vee q$

De Morgan's Laws

Definition

$\neg (p\wedge q)\equiv \neg p\vee \neg q$ $\neg (p\vee q)\equiv \neg p\wedge \neg q$

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Contraposition

Definition

$p\to q\equiv \neg q\to \neg p$

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Associative Property: $(p\vee q)\vee r\equiv p\vee (q\vee r)$

Distributive Property: $p\vee (q\wedge r)\equiv (p\vee q)\wedge (p\vee r)$