The theorems and postulates listed are the most basic relationships in Boolean algebra.
Postulate 2 (a) x + 0 = x (b) x # 1 = x
Postulate 5 (a) x + x` = 1 (b) x # x` = 0
Theorem 1 (a) x + x = x (b) x # x = x
Theorem 2 (a) x + 1 = 1 (b) x # 0 = 0
Theorem 1 (a) x + x = x (b) x # x = x
Theorem 2 (a) x + 1 = 1 (b) x # 0 = 0
Theorem 3, involution (x` ) = x
Postulate 3, commutative (a) x + y = y + x (b) xy = yx
Theorem 4, associative (a) x + (y + z) = (x + y) + z (b)= (x + y)(x + z)
Theorem 5, DeMorgan (a) (x + y)` = x` y` (b) (xy)` = x` + y `
Theorem 6, absorption (a) x + xy = x (b) x(x + y) = x
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