下列性质适用于布尔代数和布尔逻辑二者:a \lor (b \lor c) = (a \lor b) \lor c a \land (b \land c) = (a \land b) \land c 结合律a \lor b = b \lor a a \land b = b \land a 交换律a \lor (a \land b) = a a \land (a \lor b) = a 吸收律a \lor (b \land c) = (a \lor b) \land (a \lor c) a \land (b \lor c) = (a \land b) \lor (a \land c) 分配律a \lor \lnot a = 1 a \land \lnot a = 0 互补律a \lor a = a a \land a = a 等幂律a \lor 0 = a a \land 1 = a 有界律a \lor 1 = 1 a \land 0 = 0 \lnot 0 = 1 \lnot 1 = 0 0 和 1 是互补的\lnot (a \lor b) = \lnot a \land \lnot b \lnot (a \land b) = \lnot a \lor \lnot b de Morgan 定律 \lnot \lnot a = a 卷绕律(involution真值表布尔逻辑只使用两个值 0 和 1,这两个值的交集和并集可以使用真值表定义如下:\cap 0 10 0 01 0 1\cup 0 10 0 11 1 1也可以建立涉及多个输入和其他布尔运算的更复杂的真值表。