Simply the expression F = ACD +A’B +D’

Sure, let's simplify the given Boolean expression step by step.

The given expression is F = ACD + A’B + D’

Step 1: Apply the Consensus theorem

The Consensus theorem states that for three variables A, B, and C: (A AND B) OR (NOT A AND C) OR (B AND C) = (A AND B) OR (NOT A AND C)

So, we can rewrite the expression as:

F = ACD + A’B + BC

Step 2: Apply the Distributive law

The Distributive law states that A AND (B OR C) = (A AND B) OR (A AND C)

So, we can rewrite the expression as:

F = (AC AND D) OR (A' AND B) OR (B AND C)

Step 3: Apply the Absorption law

The Absorption law states that A OR (A AND B) = A

So, we can rewrite the expression as:

F = AC OR A'B OR BC

So, the simplified expression is F = AC + A’B + BC.