Question 3: A logic circuit provides the output Y as per the following truth table :
\begin{array}{|c|c|c|} \hline A & B & Y \\ \hline 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \hline \end{array}The expression for the output Y is
(1) \mathrm{A} \cdot \mathrm{B}+\overline{\mathrm{A}}
(2) A \cdot \bar{B}+\bar{A}
(3) \overline{\mathrm{B}}
(4) B
Answer: Option (3)
Explanation:
From the truth table, observe the values of output Y for different inputs A and B.
When B=0, the output Y is 1 for both A=0 and A=1.
When B=1, the output Y is 0 for both A=0 and A=1.
This shows that the output Y depends only on input B and is independent of A.
The output is 1 whenever B=0 and 0 whenever B=1,
which corresponds to the logical NOT of B.
Therefore, the Boolean expression for the output is Y=\overline{B}.
Hence, the correct answer is option (3).