Question $3-$ FOL backward chaining. We have the following information:

$-$ Vegetarians eat greens,

$-$ Broccoli are greens,

$-$ A vegetarian is a person who eats no meat,

$-$ There is a person who eats no meat,

$-$ Friends of this person do not eat meat,

$-$ Sam is friendly with a person who eats no meat.

Does anyone eat broccoli?

$1.(\backslash (40\backslash \%\backslash )$ of the credit$)$ Write down KB $($i$.$e$.$ logical representations for these sentences$),$ suitable for use with Generalized Modus Ponens. Use the following predicates: Vegetarian $\backslash (($x$)\backslash ),\backslash (\backslash$operatorname$\{$Eat$\}($x$,$ y$),\backslash$operatorname$\{$Greens$\}($x$),\backslash$operatorname$\{$Person$\}($x$),\backslash$operatorname$\{$Meat$\}($x$)\backslash ),$ and Friend $\backslash (($x$,$ y$)\backslash ).$ Note that friends are two distinct people. Also clearly Sam and broccoli are constants.

$2.(\backslash (40\backslash \%\backslash )$ of the credit$)$ Draw the proof tree generated by an exhaustive backward$-$chaining algorithm for the query $\backslash (\backslash$exists x $\backslash$operatorname$\{$Eat$\}\backslash )($brocolly$,\backslash ($ x $\backslash ))$ where clauses are matched in the order given

$3.(\backslash (20\backslash \%\backslash )$ of the credit$)$ How many solutions for $\backslash ($ x $\backslash )$ actually follow from your KB$?$ You must show how you arrived at this conclusion.