In Boolean algebra, evaluate the identity A + 1 = 1 for any Boolean variable A (domination law).

Introduction / Context:
In Boolean algebra, identities describe how logical variables combine under the OR (+) and AND (*) operations. The expression A + 1 = 1 is known as a domination (or annihilator) law for OR, asserting that ORing any Boolean variable A with logic 1 yields logic 1 regardless of the value of A. This question checks whether you recognize and correctly apply this fundamental identity used in simplifying logic expressions and digital circuits.

Given Data / Assumptions:

• A is a Boolean variable, so A can be 0 or 1.
• Symbol + denotes Boolean OR.
• We assume standard Boolean algebra axioms used in digital logic design.

Concept / Approach:
The domination law for OR states: X + 1 = 1 for any Boolean X. Intuitively, if at least one input to an OR is 1, the output is 1. Therefore, the presence of 1 renders the other input irrelevant to the final value. Recognizing this lets you immediately collapse expressions of the form A + 1 + B to 1, which is valuable in gate-level simplification.

Step-by-Step Solution:

Verification / Alternative check:
Truth table verification across A in {0, 1} confirms the identity. Alternatively, by duality, the corresponding AND annihilator is A * 0 = 0. Both are foundational and appear in standard identity sets used for Karnaugh maps and algebraic reductions.

Why Other Options Are Wrong:

• Incorrect: Contradicted by the truth table; there is no assignment making A + 1 equal 0.
• Ambiguous as stated: The operators and domain are unambiguous in Boolean algebra.
• Cannot be determined: No additional data is required; identities are universal.

Common Pitfalls:
Confusing arithmetic addition with Boolean OR; in Boolean algebra, the symbol + represents OR, not numeric addition. Also, do not assume A + 1 = A + 1 (unchanged); the law collapses it to 1 immediately.

Final Answer:
Correct