Question

Prove algebraically that (X + Y)(X + Z) = X + YZ

Answer 1

L.H.S. = (X + Y)(X + Z) = XX + XZ + XY + YZ

= X + XZ + XY + YZ  (XX = X Indempotence law)

= X + XY + XZ + YZ = X(1 + Y) + Z(X + Y)

= X.1 + Z(X + Y)   (1 + Y = 1 property of 0 and 1)

= X + XZ + YZ)   (X . 1 = X property of 0 and 1)

= X(1 + Z) + YZ 

= X.1 + YZ    (1 + Z = 1 property of 0 and 1) 

= X.1 + YZ    (X . 1 = X property of 0 and 1)

= L.H.S. Hence proved