Idempotent Law – An input that is AND´ed or OR´ed with itself is equal to that input
A + A = A A variable OR’ed with itself is always equal to the variable
A . A = A A variable AND’ed with itself is always equal to the variable
Proof:
x + x = (x + x) • 1 (1 is the identity for AND)
= (x + x) • (x + x') (Complement, x + x' = 1)
= x + (x • x') (OR distributes over AND)
= x + 0 (Complement, x • x' = 0)
= x (0 is the identity for OR)