Question

The logical expression \( X \), in its simplest form for the truth table \[ \begin{array}{|c|c|c|} \hline A & B & X \\ \hline 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ 1 & 1 & 1 \\ \hline \end{array} \] is

• A. \( X = a \cdot b \)
• B. \( X = a + b \)
• C. \( X = a \cdot b' \)
• D. \( X = a' \cdot b \)

Hint:

The truth table can be used to derive the logical expression using standard Boolean operations.

Answer 1

The Correct Option is C

Step 1: Analyze the Truth Table.
From the truth table, it is evident that \( X \) is true when \( A \) is true and \( B \) is false. Therefore, the expression for \( X \) is \( X = a \cdot b' \).
Step 2: Conclusion.
The correct answer is (C), \( X = a \cdot b' \).