To solve this problem, we need to determine the logic expression that matches the given truth table.$\\$The truth table is:$\\ \begin{array}{ccc} A & B & Y \\ 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{array} \\$From the truth table, we can derive the expression for $Y$ by analyzing when $Y = 1. \\$The rows where $Y = 1$ are:$\\$• When $A = 0$ and $B = 0 \\$• When $A = 1$ and $B = 0 \\$We can write the expression for $Y$ as:$\\ Y = \bar{A} \bar{B} + A \bar{B} \\$Factor out $\bar{B}: \\ Y = \bar{B} (\bar{A} + A) \\$Since $\bar{A} + A = 1,$ we have:$\\ Y = \bar{B} \\$Therefore, the logic expression that matches the truth table is $\bar{B}. \\$This corresponds to Option 1.