. Simplify the expression F = A B D+A B' using Boolean identities

To simplify the Boolean expression F = A B D + A B', we can use the Boolean identities. Here are the steps:

1. Apply the Consensus theorem which states that (A AND B) OR (NOT B AND A) = A.

So, F = A B D + A B' simplifies to F = A.

Therefore, the simplified form of the given Boolean expression is F = A.

To simplify the Boolean expression F = A B D + A B', we can use the Boolean identities. Here are the steps:

1. Apply the Consensus theorem which states that A B + A' C + B C = A B + A' C. In this case, A = A, B = B, and C = D. So, A B D + A B' = A B + A B' D.

2. Now, apply the Absorption law which states that A + A B = A. In this case, A = A B and B = A B' D. So, A B + A B' D = A B.

So, the simplified expression of F = A B D + A B' is F = A B.