2. Simplify the expression F = A B D+A B' using Boolean identities.3. Reduce A (A + B) to the least number of terms.4. Simplify the expression F=A B ' D+A B' D'Short answer questions:1. Simplify the following expressions using boolean laws.𝐹 = 𝐴. 𝐵 + 𝐴 . (𝐶. 𝐷 + 𝐶. 𝐷 ) 𝐹 = 𝐴. 𝐵. 𝐶 + 𝐴 + 𝐴. 𝐶. 𝐵Long answer questions:𝐴 + 𝐵 . (𝐶 + 𝐷)F = 𝐴.(A+B)+𝐴. 𝐵

Sure, here are the simplified expressions:

2. F = A B D + A B' can be simplified to F = A B' + B D using the Consensus theorem.

3. A (A + B) can be simplified to A using the Absorption law.

4. F = A B' D + A B' D' can be simplified to F = A B' using the Consensus theorem.

Short answer questions:

1. F = A. B + A . (C. D + C. D ) can be simplified to F = A. B + A. C. D using the Idempotent law.

   F = A. B. C + A + A. C. B can be simplified to F = A + B. C using the Consensus theorem.

Long answer questions:

A + B . (C + D) can be simplified to A + B. C + B. D using the Distributive law.

F = A.(A+B)+A. B can be simplified to F = A + A. B using the Absorption law, and then further simplified to F = A using the Idempotent law.