R$1$: Soda $(x{)}^{{?}^{{?}^{?}}}ps(y)$ 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$)$

a$.$ 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.

b$.$ 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.