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Apply the absorption law: The Boolean expression C + C*D simplifies to ________.

Difficulty: Easy

C
D
C + D
1
C * D

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:

Expression is C + C*D.
Operators: + is OR, * is AND.

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.

Apply the absorption law: The Boolean expression C + C*D simplifies to ________.

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