Step 1: Understanding the Concept:
A NAND gate is a universal digital logic gate. The term "NAND" is a contraction of "NOT AND", meaning its output is the exact opposite of an AND gate.
Step 2: Key Formula or Approach:
The logical AND operation for two inputs $A$ and $B$ is written as $A \cdot B$ or $AB$.
The logical NOT operation, which signifies inversion, is represented by a horizontal line (bar) over the expression.
Step 3: Detailed Explanation:
To construct the expression for a NAND gate, we first take the AND operation of inputs $A$ and $B$, which gives $AB$.
Next, we apply the NOT operation to this result to invert it.
This results in placing a bar over the entire AND expression, giving:
\[ Y = \overline{AB} \]
Reviewing the other options:
(A) $Y = A + B$ is the expression for an OR gate.
(B) $Y = AB$ is the expression for an AND gate.
(D) $Y = \overline{A + B}$ is the expression for a NOR gate.
Step 4: Final Answer:
The correct option is (C).