Absorption law check in Boolean algebra Verify whether the Boolean identity AC + ABC = AC holds true, and select the correct truth status.

Introduction / Context:Recognizing core Boolean identities accelerates simplification of digital logic. The expression AC + ABC can often be reduced using the absorption law, which helps remove redundant product terms and minimize gate counts.

Given Data / Assumptions:

• Boolean variables A, B, C ∈ {0,1}.
• + denotes OR; juxtaposition (e.g., AB) denotes AND.
• We test identity: AC + ABC ?= AC.

Concept / Approach:The absorption law states X + XY = X. Here, let X = AC and Y = B. Then AC + ABC = X + XY = X, which equals AC. Thus the extra term ABC is redundant, and the identity is true.

Step-by-Step Solution:Start: AC + ABC.Factor AC: AC(1 + B).Use 1 + B = 1 (since 1 OR B = 1).Therefore AC(1) = AC.

Verification / Alternative check:Truth table reasoning: whenever AC = 0, both sides are 0. Whenever AC = 1, the left side is 1 (either via AC or ABC), and the right side is 1. Hence both sides match for all assignments of A, B, C.

Why Other Options Are Wrong:

• False: contradicts the absorption law; no counterexample exists.

Common Pitfalls:

• Assuming ABC contributes additional minterms beyond AC; in fact ABC is contained within AC.
• Forgetting the identity 1 + B = 1, key to the factorization step.

Final Answer:True