The output Y of following circuit for given inputs is :

Solution

Physics sir · 3 steps

Write each gate's output, then AND them: every term carries a variable times its own complement.

1. Top gate. The OR gate gets A directly and B through a NOT gate. Its output is A + B̄.
2. Bottom gate. The lower AND gate gets B directly and A through a NOT gate. Its output is Ā · B.

   Y = (A + B̄) · ĀB = AĀB + ĀBB̄ = 0 + 0 = 0

   A, B	A + B̄	Ā · B	Y
   0, 0	1	0	0
   0, 1	0	1	0
   1, 0	1	0	0
   1, 1	1	0	0

3. So. The lower gate gives 1 only when A = 0 and B = 1, and that is exactly when the upper gate gives 0. The final AND never sees two 1s, so Y = 0 always, which is option (d).

The idea to keep. Label the output of every gate before you simplify. Then use XX̄ = 0: any product containing a variable and its complement drops out.

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