Answer
Showing that in a Boolean algebra, the idempotent laws
x ∨ x = x and x ∧ x = x hold for every element x.
Work Step by Step
By the domination, distributive, and identity laws,
x∨x = (x∨x)∧1 = (x∨x)∧(x∨x) = x ∨ (x ∧ x) = x ∨ 0 = x.
Similarly,
x ∧ x =(x ∧ x) ∨ 0=(x ∧ x) ∨ (x ∧ x) = x ∧ (x ∨ x) = x ∧ 1 = x.
