AAx,$yP(x,y{)}^{{?}^{?}}Q(y,x)=>R(x,y)$

AAx,$y(x,$Bob${)}^{{?}^{?}}S(y,x)=>P(x,y)$

AAx,$yS(x,y)=>Q(y,x)$

AAx,$y(x,y,x)=>Q(x,y)$

AAx,$yT(x,x,y)=>Q(x,y)$

$T($ Alice,Dawn,Alice$)$

$T(Eve,$Carl,Eve$)$

$T(Alice,$Bob,Dawn$)$

$T(Carl,$Carl,Alice$)$

$S(Bob,$Alice$)$

$S(Carl,$Bob$)$

$S(Dawn,$Carl$)$

$S(Carl,$Dawn$)$

$S(Alice,$Dawn$)$

$S(Eve,$Carl$)$

Use backward chaining to find ALL answers for the following queries. When matching rules, proceed

from top to bottom. You must show your search tree. Each node should contain a list of subgoals

remaining to be proven. Also label each arc with the rule that was matched and give the substitutions that

permit the match.

a$)$ Alice, $x$

b$)$ EEx,$yR(x,y).$