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Three-input AND expression: Evaluate the statement: “The Boolean expression for a three-input AND gate with inputs A, B, C and output X is X = ABC.”

Difficulty: Easy

Correct
Incorrect
Only true for NAND gates
Not enough information is provided

Correct Answer: Correct

Explanation:

Introduction / Context:
Understanding gate-level Boolean expressions is essential for simplification, implementation, and verification. A multi-input AND gate outputs HIGH only if all inputs are HIGH.

Given Data / Assumptions:

Inputs: A, B, C.
Gate: AND (not NAND or OR).
Output: X.

Concept / Approach:
The AND operation corresponds to logical multiplication. For three inputs, the output is the logical product of all three: X = A * B * C. Conventionally the multiplication sign is omitted, so X = ABC is standard shorthand.

Step-by-Step Solution:

Recall: AND truth condition → all inputs must be 1 for output 1.Write expression: X = A * B * C = ABC.Confirm with sample: if any input = 0, product = 0.

Verification / Alternative check:
Truth table rows with any 0 input lead to X = 0; only A=1, B=1, C=1 yields X=1, matching ABC.

Why Other Options Are Wrong:

Incorrect: Conflicts with standard AND definition.Only true for NAND gates: NAND is the complement of AND, not identical.Not enough information: Gate type is stated; that is sufficient.

Common Pitfalls:
Confusing AND with OR; forgetting implied multiplication in Boolean notation; mixing up AND and NAND.

Three-input AND expression: Evaluate the statement: “The Boolean expression for a three-input AND gate with inputs A, B, C and output X is X = ABC.”

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