From the given truth table, we can observe the relationship between the inputs ($A$, $B$) and the output ($Y$): When $B = 0$, output $Y = 1$ (irrespective of $A$). When $B = 1$, output $Y = 0$ (irrespective of $A$). Since the output $Y$ is always the exact complement of input $B$ and is completely independent of the state of input $A$, the Boolean expression for the output is $Y = \bar{B}$.