Discussion
A logic gate circuit is shown in the figure below. The correct combination for the input \((P, Q)\) for which the output \(T = 1\) is
Answer: A
The output is 1 only for \((P, Q) = (0, 0)\).
The upper branch gives \(\overline{P + Q}\) (OR followed by NOT, a NOR), and the lower branch gives \(\overline{Q}\). The AND gate combines them:
\[ \begin{aligned} T &= \overline{P + Q} \cdot \overline{Q} \\ &= \overline{P}\,\overline{Q} \cdot \overline{Q} = \overline{P}\,\overline{Q} \end{aligned} \]
So \(T = 1\) only when both inputs are 0. For (0,1), (1,1) and (1,0) at least one input is 1, the NOR output is 0, and the AND gate gives 0.
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