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

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.