To solve this problem, we need to analyze the given logic circuit.$\\$The circuit consists of:$\\$• An OR gate with inputs $A$ and $B. \\$• An AND gate with inputs from the OR gate and input $C. \\$The output of the OR gate is:$\\ O_{OR} = A + B \\$The output of the AND gate is:$\\ Y = O_{OR} \cdot C = (A + B) \cdot C \\$We want the output $Y = 1. \\$For the AND gate to output 1, both inputs must be 1:$\\ 1. (A + B) = 1 \\ 2. C = 1 \\$Let's analyze the options:$\\$Option 1: $A = 1, B = 1, C = 0 \\ (A + B) = 1 + 1 = 1, \, C = 0 \\ Y = 1 \cdot 0 = 0 \\$Option 2: $A = 1, B = 0, C = 1 \\ (A + B) = 1 + 0 = 1, \, C = 1 \\ Y = 1 \cdot 1 = 1 \\$Option 3: $A = 0, B = 1, C = 0 \\ (A + B) = 0 + 1 = 1, \, C = 0 \\ Y = 1 \cdot 0 = 0 \\$Option 4: $A = 1, B = 0, C = 0 \\ (A + B) = 1 + 0 = 1, \, C = 0 \\ Y = 1 \cdot 0 = 0 \\$The correct option is Option 2: $A = 1, B = 0, C = 1. \\$