Consider the following logic circuit.
The output is Y = 0 when :

Solution

Physics sir · 3 steps

A NAND gives 0 only when both of its inputs are 1, so find when both feeding gates give 1.

1. Read the circuit. The top gate is AND with output AB. The bottom gate is OR with inputs B and Ā, so its output is B + Ā. Both feed a NAND, so Y = AB · (B + Ā)̅.
2. Simplify. Expand: AB · B + AB · Ā = AB + 0 = AB, because B · B = B and A · Ā = 0. So the whole circuit is a NAND of A and B.

   Y = A̅B̅

   Option	AB	B + Ā	Y
   (a) A = 1, B = 0	0	0	1
   (b) A = 0, B = 0	0	1	1
   (c) A = 1, B = 1	1	1	0
   (d) A = 0, B = 1	0	1	1

3. So. Both NAND inputs are 1 only when A = 1 and B = 1, so Y = 0 only for option (c).

The idea to keep. For a NAND at the output, ask when every input to it is 1. Write the Boolean expression and simplify with AĀ = 0 and BB = B before checking cases.

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