論理演算
吸収則
p ∨ ( p ∧ q ) ≡ p p ∧ ( p ∨ q ) ≡ p {\displaystyle {\begin{aligned}p\lor (p\land q)&\equiv p\\p\land (p\lor q)&\equiv p\\\end{aligned}}}
ド・モルガンの法則
¬ ( p ∨ q ) ≡ ( ¬ p ) ∧ ( ¬ q ) ¬ ( p ∧ q ) ≡ ( ¬ p ) ∨ ( ¬ q ) {\displaystyle {\begin{aligned}\lnot (p\lor q)&\equiv (\lnot p)\land (\lnot q)\\\lnot (p\land q)&\equiv (\lnot p)\lor (\lnot q)\\\end{aligned}}}
その他
p ∨ 0 ≡ p p ∧ 0 ≡ 0 p ∨ 1 ≡ 1 p ∧ 1 ≡ p p ∨ ( ¬ p ) ≡ 1 p ∧ ( ¬ p ) ≡ 0 ¬ ( ¬ p ) ≡ p {\displaystyle {\begin{aligned}&p\lor 0\equiv p\\&p\land 0\equiv 0\\&p\lor 1\equiv 1\\&p\land 1\equiv p\\&p\lor (\lnot p)\equiv 1\\&p\land (\lnot p)\equiv 0\\&\lnot (\lnot p)\equiv p\\\end{aligned}}}