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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.

Edited by vishalonne

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