Prove the identity of following Boolean equation AABASolutio

Prove the identity of following Boolean equation:

A+A*B=A

Solution

When A = 0 ,B = 0 :

A * B = 0 * 0 = 0

A+A*B = 0 + 0 = 0

i.e., A + A*B = A

When A = 0 ,B = 1 :

A * B = 0 * 1 = 0

A+A*B = 0 + 0 = 0

i.e., A + A*B = A

When A = 1 ,B = 0 :

A * B = 1 * 0 = 0

A+A*B = 1 + 0 = 1

i.e., A + A*B = A

When A = 1 ,B = 1 :

A * B = 1 * 1 = 1

A+A*B = 1 + 1 = 1

i.e., A + A*B = A

Hence proved.