The truth table for the given logic circuit is

The truth table for the given logic circuit is

  1. P
  2. Q
  3. S
  4. R

Solution

From the logic circuit, $\mathrm{Y}=\overline{(\overline{\mathrm{A}+\mathrm{B}}) \cdot(\mathrm{A} \cdot \mathrm{~B})}$
Using De-Morgan's law, $\overline{\mathrm{A}+\mathrm{B}}=\overline{\mathrm{A}} \cdot \overline{\mathrm{B}}$ $\begin{aligned} & \mathrm{Y}=\overline{(\overline{\mathrm{A}} \cdot \overline{\mathrm{~B}}) \cdot(\mathrm{A} \cdot \mathrm{~B})} \\ & \mathrm{Y}=\overline{(\overline{\mathrm{A}} \cdot \mathrm{~A}) \cdot(\overline{\mathrm{B}} \cdot \mathrm{~B})} \\ & \mathrm{Y}=\overline{0.0}=1 \end{aligned}$ $\therefore \quad$ Output is always 1. ~

Asked in: MHT CET 2024 (04 May Shift 2)

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