$($i$)$ A knowledgebase $($KB$)$ has the following hom clauses

AI: $-av-bvd$

A$2$: $-dvvf$

A$3$: $-dvv-rvg$

A$4$: $-bVVVc$

Also, the following facts are present in the KB

Fl: a

F$2$:b

F$3$: $C$

Derive the sentence $"g"$ by applying data driven and goal driven inference techniques. $(9$ marks$)$

$($ii$)$ Represent the given sentence $"$If the sun is shining, then I am going to the ball game" in propositional logic. Check if the negation of the given sentence is equivalent to "The sun is shining, and I am not going to the ball game." $(6$ marks$)$