Boolean basics refresher: What is the correct Boolean expression for the output X of a three-input AND gate with inputs A, B, and C?

Introduction / Context:Understanding standard Boolean notation is essential for reading data sheets and designing logic. The AND function outputs logic 1 only when all inputs are 1.

Given Data / Assumptions:

• Three inputs: A, B, C.
• Standard Boolean operators: “·” (AND), “+” (OR), and overbar/apostrophe for NOT.

Concept / Approach:The n-input AND gate is expressed as a product of the inputs. Therefore, a three-input AND is X = A · B · C.

Step-by-Step Solution:Identify gate → AND.Use product form → multiply all inputs.Result → X = A · B · C.

Verification / Alternative check:Truth table shows X = 1 only for A = B = C = 1, matching the product term behavior.

Why Other Options Are Wrong:A + B + C: OR function, not AND.A – B – C and A $ B $ C: nonstandard/incorrect operators.X = A(B + C): mixed expression that does not require all three inputs to be 1.

Common Pitfalls:Confusing sum (OR) with product (AND) notation.

Final Answer:X = A · B · C