$(9$ pt$)$ Perform $\backslash$beta $-$reduction for the following $\backslash$lambda expressions.

$($a$)(3$ pt$)((\backslash$lambda $($x$)($x y$))(\backslash$lambda $($z$)$ z$))$

$($b$)(3$ pt$)(((\backslash$lambda $($x$)(\backslash$lambda $($y$)($y$)))((\backslash$lambda $($z$)$ z$)$ a$))$ b$)$

$($c$)(3$ pt$)((\backslash$lambda $($x$)$ x$)((\backslash$lambda $($y$)$ y$)(((\backslash$lambda $($v$)(\backslash$lambda $($w$)$ w$))$ a$)$ b$)))$

Summer $2024$ page $1$ of $2$