Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): A logic circuit with the Boolean expression Y = A + A B is equivalent to an OR gate. Reason (R): The simplification of the expression A + A B to A + B is a direct consequence of De Morgan's laws. In the light of the above statements, choose the most appropriate answer from the options given below:

Step-by-step solution

Assertion (A) is true: The Boolean expression Y = A + A B can be simplified using the distributive law of Boolean algebra, which states that A + BC = (A + B)(A + C) . Applying this, A + A B = (A + A )(A + B) . Since A + A = 1 , the expression becomes 1 (A + B) = A + B . The expression Y = A + B represents an OR gate. Thus, the logic circuit is equivalent to an OR gate. Reason (R) is false: The simplification of A + A B to A + B relies on the distributive law ( A + BC = (A + B)(A + C) ) and the OR law ( A + A = 1 ),