$5.(15$pt$)$ Consider the following grammar, G:

$1.$ P $->$ S $$

$2.$ S $->$ if $($e$)$ then M O

$3.$ S $->$ other

$4.$ M $->$ if $($e$)$ then M else M

$5.$ M $->$ other

$6.$ O $->$ else T

$7.$ O $->\backslash$epsi

$8.$ T $->$ if $($e$)$ then T

$9.$ T $->$ other

$($a$)(5$pt$)$ Compute the sets first$($X$)$ and follow$($X$),$ for all non$-$terminals X$,$ and the sets

predict$($p$)$ for all production rules p$.$

$($b$)(5$pt$)$ Prove that G an LL$(1)$ grammar.

$($c$)(5$pt$)$ We said that there is no top$-$down grammar for if$..$then..else statements. Does G

contradict this? Prove your answer.