To solve this problem, we need to analyze the given logic circuit.$\\$The circuit consists of:$\\$• Two inputs, $A$ and $B. \\$• Two NOT gates (inverters) connected to each input.$\\$• An OR gate followed by a NOT gate (NOR gate).$\\$Let's determine the output $Y$ for each combination of inputs $A$ and B:} \\ 1. When $A = 0$ and $B = 0: \\$• NOT gate outputs: $\overline{A} = 1, \overline{B} = 1. \\$• OR gate output: $\overline{A} + \overline{B} = 1 + 1 = 1. \\$• NOR gate output: $Y = \overline{(1)} = 0. \\$2. When $A = 0$ and $B = 1: \\$• NOT gate outputs: $\overline{A} = 1, \overline{B} = 0. \\$• OR gate output: $\overline{A} + \overline{B} = 1 + 0 = 1. \\$• NOR gate output: $Y = \overline{(1)} = 0. \\$3. When $A = 1$ and $B = 0: \\$• NOT gate outputs: $\overline{A} = 0, \overline{B} = 1. \\$• OR gate output: $\overline{A} + \overline{B} = 0 + 1 = 1. \\$• NOR gate output: $Y = \overline{(1)} = 0. \\$4. When $A = 1$ and $B = 1: \\$• NOT gate outputs: $\overline{A} = 0, \overline{B} = 0. \\$• OR gate output: $\overline{A} + \overline{B} = 0 + 0 = 0. \\$• NOR gate output: $Y = \overline{(0)} = 1. \\$The truth table for the circuit is:$\\ \begin{array}{c|c|c} A & B & Y \\ \hline 0 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ 1 & 1 & 1 \\ \end{array} \\$This corresponds to Option 4.