The truth table for this given circuit is :

Solution

Physics sir · 2 steps

Write the Boolean expression gate by gate; the A and NOT A terms cancel out, and Y is just B.

1. Read each gate. The top AND gate gets A and B, so it gives AB. The bottom AND gate gets A̅ (through the NOT gate) and B, so it gives A̅B. The hop where the wires cross means they are not joined.

   Y = AB + A̅B = B(A + A̅) = B · 1 = B

   A, B	AB	A̅B	Y = AB + A̅B
   0, 0	0	0	0
   0, 1	0	1	1
   1, 0	0	0	0
   1, 1	1	0	1

2. So. The output column reads 0, 1, 0, 1, which is exactly Y = B. That matches option (b).

The idea to keep. For a gate circuit, write the output of each gate as an expression, then simplify with A + A̅ = 1. The simplified form often gives the whole truth table in one line.

Answer from the NTA final answer key. Solution by PrepWiser.