Controversy on truth table. X+ X’.Y=X+Y

[vishalon]

Question. Name the law given and verify it using a truth table. X+ X’.Y=X+Y

 

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 complementary law)

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

= R.H.S. Hence proved.

 

My teacher marked my answer WRONG. And told me to find the correct answer. Friends tell me is it a complementary law or distributive law or Absorption law? If it is absorption kindly tell me how to prove RHS and LHS algebraically.

 

Thank you for any advice or suggestions.