The output (Y) of logic circuit given below is 0 only when :

Solution

Physics sir · 3 steps

An AND gate with one input fixed at 1 just passes the other input through, so the circuit collapses.

1. Simplify the AND. The lower gate is an AND with inputs B and 1. Since B · 1 = B, its output is B itself.
2. Combine at the end. The upper OR gate gives A + B. The final OR gate adds the two branches, and B + B = B in Boolean algebra.

   Y = (A + B) + (B · 1) = A + B + B = A + B

   A	B	A + B	B · 1	Y
   0	0	0	0	0
   0	1	1	1	1
   1	0	1	0	1
   1	1	1	1	1

3. So. The whole circuit behaves as a single OR gate, and an OR gate gives 0 only when every input is 0. That means A = 0 and B = 0, which is option (a).

The idea to keep. Before building a truth table, simplify: X · 1 = X, X + 0 = X and X + X = X. A messy-looking circuit often reduces to one basic gate.

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