Boolean expression recall: Write the standard Boolean equation for the output X of a 3-input AND gate with inputs A, B, and C.

Introduction / Context:Boolean equations compactly describe logic behavior and map directly to gate-level implementations. Being able to write the correct expression for common gates like a 3-input AND is essential for circuit analysis, HDL coding, and testbench verification.

Given Data / Assumptions:

• Three inputs: A, B, C.
• One output: X.
• Standard notation: juxtaposition or the dot “·” denotes AND; plus “+” denotes OR.

Concept / Approach:An AND gate outputs HIGH only when all inputs are HIGH. The Boolean product of all inputs captures this requirement: X equals A AND B AND C, written as X = A·B·C or simply X = ABC (when the AND operator is implied by concatenation).

Step-by-Step Solution:Identify operation: AND across three variables.Write product: X = A·B·C.Use concise form: X = ABC (common shorthand).Therefore, the correct expression is X = ABC.

Verification / Alternative check:Truth table: only when A=1, B=1, and C=1 does the product evaluate to 1; in all other cases, at least one factor is 0, producing X=0.

Why Other Options Are Wrong:

• X = AB omits C and represents a 2-input AND.
• X = A + B + C is a 3-input OR, not AND.
• X = AB + C equals (A AND B) OR C, which differs from pure 3-way AND.

Common Pitfalls:

• Dropping inputs unintentionally when moving from schematic to equation.
• Confusing additive and multiplicative operators in Boolean algebra.

Final Answer:X = ABC