Which of the following Boolean algebraic equation(s) is/are CORRECT?

Correct Answer: (B), (C), (D)Option B — TRUE: AB + AC + BC. By Consensus Theorem: xy + x̄z + yz = xy + x̄z (consensus term yz is redundant). Here x=A, y=B, z=C: AB + ĀC + BC = AB + ĀC. ✓Option C — TRUE: (Ā+C)(A+B) = ĀA + ĀB + CA + CB = ĀB + AC + BC. By consensus (same theorem): ĀB + AC + BC = ĀB + AC. The expression given includes BC which is the consensus term — the equation holds. ✓Option D — TRUE: Through Boolean algebraic manipulation, the LHS simplifies to AD + C̄D. Verified in ACE solution. ✓Option A — FALSE: LHS simplifies to a different expression than B̄C + AB.

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