Difficulty: Easy
Correct Answer: C
Explanation:
Introduction / Context:This tests the absorption law in Boolean algebra, which captures how a term absorbs a more specific version of itself when combined by OR.
Given Data / Assumptions:
Concept / Approach:Absorption: X + X*Y = X. Intuitively, when X is true, X*Y is redundant; when X is false, X*Y is also false. Therefore, the more general term X alone suffices to represent the logic.
Step-by-Step Solution:
Step 1: Identify X with C and Y with D.Step 2: Apply X + X*Y = X → C + C*D = C.Step 3: Verify by truth table if desired.Verification / Alternative check:Constructing a truth table shows output equals C for all D values.
Why Other Options Are Wrong:
D: Output cannot depend solely on D.C + D: Overstates the function; equals C only when D=0.1: Would be true for all inputs, not equivalent.C * D: Too restrictive; misses cases where C=1, D=0.Common Pitfalls:Confusing absorption with consensus; remember the exact identity.
Final Answer:C
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