Complete the proof of Theorem 15.3. Theorem 15.3: (a) x 0 = 0 (a)ʹ x + 1 = 1 Dominance Laws (b) x(x + y)

Complete the proof of Theorem 15.3.
Theorem 15.3:
(a) x ˆ™ 0 = 0
(a)ʹ x + 1 = 1 Dominance Laws
(b) x(x + y) = x bf x xy = x Absorption Laws
(c) [xy = xz and y = z] ‡’ y = z Cancellation Laws
(c)ʹ [x + y = x + z and + y = + z] ‡’ y = z
(d) x(yz) = (xy)z
(d)ʹ x + (y + z) = (x + y) + z Associative Laws
(e) [x + y = 1 and xy = (0] ‡’ y = Uniqueness of Complements (Inverses)

(g) = +

(h) = 1
(h)ʹ = 0
(i) x = 0 if and only if xy = x
(i)ʹ x + = 1 if and only if x + y = x

x+y xy