Question

Prove : X + X’Y = X + Y (Algebraic method)

Answer 1

My Answer.

X Y X’ X’.Y X+X’.Y X+Y

0 0 1 0 0 0

0 1 1 1 1 1

1 0 0 0 1 1

1 1 0 0 1 1

Prove algebraically that X + X’Y = X + Y.

L.H.S. = X + X’Y

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

= X(1 + Y) + X’Y (1 + Y = 1 property of 0 and 1)

= X + XY + X’Y

= X + Y(X + X’)

= X + Y.1 (X + X’ =1 complementarity law)

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

= R.H.S. Hence proved.