Answer
Showing that in a Boolean algebra, if x ∨ y = 0, then x = 0
and y = 0, and that if x ∧ y = 1, then x = 1 and y = 1.
Work Step by Step
-- hypotheses, and the distributive law it follows
that x = x ∨ 0 = x ∨ (x ∨ y) = (x ∨ x) ∨ y = x ∨ y = 0.
Similarly,
-- y = 0. To prove the second statement,
-note that
x = x∧1 = x∧(x∧y) = (x∧x)∧y = x∧y = 1.
-Similarly,
y = 1.
