The equation A+(AB) =A, pertaining to the law of ABSORPTION, is
shown below with the corresponding logic diagram and truth table.
As shown by the truth table above, the AND-gate input A and the
OR-gate output A+(AB) are equal (identical) in every case.
Therefore, A+(AB) is equal to A. Any Boolean expression in the
form of A+ (AB) can be simplified by using the law of
ABSORPTION. Any variable or quantity ORed with an ANDed
output which contains that variable or quantity will absorb the
ANDed output. (Refer to the logic diagram above.) For example,
the Boolean expression C+(XDC) can be simplified to a single C
variable, because the ANDed output (XDC) contains the same C
variable and is effectively absorbed.