Write the inverter relationship: For a NOT (inverter) logic gate with input C and output Y, which Boolean expression correctly represents the function?

Introduction / Context:An inverter (NOT gate) outputs the logical complement of its input. Fluency with equivalent notations is essential: apostrophe ('), overbar, and the keyword NOT all mean logical negation.

Given Data / Assumptions:

• Single input C and single output Y.
• Standard Boolean shorthand is allowed (apostrophe to denote complement).

Concept / Approach:If the input is 1, the output must be 0, and vice versa. The concise expression is Y = C' (read as “Y equals C complement”). Textbooks may also write Y = NOT C or place a bar over C.

Step-by-Step Solution:Identify function: inverter.Apply complement: Y equals the logical NOT of C.Choose compact notation: Y = C'.

Verification / Alternative check:Truth table confirms that when C = 0 → Y = 1, and when C = 1 → Y = 0, exactly matching a complement.

Why Other Options Are Wrong:Y = C: that is a buffer, not an inverter.Y = NOT C: conceptually correct, but the question expects a compact Boolean expression; we accept apostrophe form.Y = C XOR 1: equals C' only if XOR is interpreted as inversion, but XOR with 1 in Boolean algebra does invert; however, that is not standard notation for expressing a NOT gate block symbolically.Y = C + C: simplifies to C, not an inversion.

Common Pitfalls:Confusing complement notation and using ambiguous arithmetic symbols instead of Boolean notation.

Final Answer:Y = C'