$3.($Chap$.2,10$ points, $5$ points each$)$

For each pair of libraries below, state whether or not $\backslash (\backslash$mathcal$\{$L$\}\_\{\backslash$text $\{$left $\}\}\backslash$equiv $\backslash$mathcal$\{$L$\}\_\{\backslash$text $\{$right $\}\}\backslash )($interchangeable$).$

If so$,$ show how they assign identical probabilities to all outcomes. If not, describe a successful distinguisher and compute its output probabilities when linked to the two libraries.

$($a$)$

$($b$)$

$($Note that $\backslash ($ x $\backslash )$ and $\backslash ($ y $\backslash )$ are swapped in the first two lines, but not in the return statement.$)$