Consider the following Prolog facts and rules:

membr$($H$,[$H$|\_]).$

membr$($H$,[\_|$T$])$ :$-$ membr$($H$,$ T$).$

unique$($X$,[$H$|$T$])$ :$-$ not$($X$=$H$),$ unique$($X$,$ T$).$

unique$($H$,[$H$|$T$])$ :$-$ not$($membr$($H$,$ T$)).$

Draw the Prolog tree corresponding to each of the following queries, explaining the effect of each

cut:

$($a$)(15$pt$)$

$?-$ membr$($a$,[$a$,$b$,$a$]).$

true ;

true ;

false.

$($b$)(17$pt$)$

$?-$ unique$($a$,[$b$,$a$,$c$]).$

true ;

false.

$($c$)(18$pt$)$

$?-$ unique$($a$,[$a$,$b$,$a$]).$

false.