$6$: $($Bonus$)$ not a must: Assume KB consists of the following rules:

R$1$: Soda$($x$)^$ Chips$($y$)6$: $($Bonus$)$ not a must: Assume KB consists of the following rules:

R$1$: Soda$($x$)^$ Chips$($y$)$ Cheaper$($x$,$ y$)$

R$2$: Chips$($x$)^$ Cereals$($y$)$ Cheaper$($x$,$ y$)$

R$3$: Cheaper$($x$,$ y$)^$ Cheaper$($y$,$ z$)$ Cheaper$($x$,$ z$)$

And the facts:

F$1$: Soda$($Sprite$)$

F$2$: Chips$($Ruffles$)$

F$3$: Cereals$($Cheerios$)$

F$4$: Cereals$($MiniWheats$)$

Assume that all facts F$1-$F$4$ are known at the beginning of the inference process. Illustrate the process of forward chaining by listing all newly inferred facts. Assume that both rules and facts are matched and tried in the order of their appearance.

Show how to prove Cheaper$($Sprite$,$ Cheerios$)$ using backward chaining and the KB given in part a$.$ Draw the graph for the problem, assuming rules and facts are tried and matched in the order given.$$ Cheaper$($x$,$ y$)$

R$2$: Chips$($x$)^$ Cereals$($y$)$ Cheaper$($x$,$ y$)$

R$3$: Cheaper$($x$,$ y$)^$ Cheaper$($y$,$ z$)$ Cheaper$($x$,$ z$)$

And the facts:

F$1$: Soda$($Sprite$)$

F$2$: Chips$($Ruffles$)$

F$3$: Cereals$($Cheerios$)$

F$4$: Cereals$($MiniWheats$)$

Assume that all facts F$1-$F$4$ are known at the beginning of the inference process. Illustrate the process of forward chaining by listing all newly inferred facts. Assume that both rules and facts are matched and tried in the order of their appearance.

Show how to prove Cheaper$($Sprite$,$ Cheerios$)$ using backward chaining and the KB given in part a$.$ Draw the graph for the problem, assuming rules and facts are tried and matched in the order given.