Question

Prove the following rules using the proof of perfect induction

a. XY’ + XY = X
b. X + Y = Y + X

Answer 1

a. XY’ + XY = X

By proof of perfect induction X = 0, Y =1 XY’ + XY = X

LHS = 0.0 + 0.1±0 + 0 = 0

By proof of perfect induction X = 1, Y = 0 LHS = 1.1+ 1.0 = 1 + 0 = 1

b. X + Y = Y + X

By proof of perfect induction X = 0, Y = 1 LHS = 0 + 1 = 1 RHS = 1 + 0 =1 LH S = RHS

By proof of perfect induction X = 1, Y = 0 LHS = 1 + 0 = 1 RHS = 0 + 1 = 1 LHS = RHS