**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)