\[ Y = (A + B\overline{C})(\overline{A}B + C) \] \[ \begin{aligned} Y &= A(\overline{A}B + C) + B\overline{C}(\overline{A}B + C)\\[4pt] &= A\overline{A}B + AC + \overline{A}BB\overline{C} + B\overline{C}C\\[4pt] &= 0 + AC + \overline{A}B\overline{C} + 0\\[4pt] &= AC + \overline{A}B\overline{C} \end{aligned} \] \[ \boxed{\,Y = A\,C \;+\; \overline{A}\,B\,\overline{C}\,} \]