Consider the following statements about the types of fruit people like.

If people like apples, then they do not like oranges. If people do not like apples, then they like oranges and grapes. If people do not like oranges or they like grapes, then they like pears. If people like pears, then they like bananas.

a. Express the above statements in propositional logic. Clearly define the meaning of your propositional symbols.

b. Convert your statements from (a) into conjunctive normal form (CNF). Number the clauses in your knowledge base (KB) starting with number 1.

c. Using proof by refutation and resolution, try to prove that people like bananas using your KB from (b). For each new clause in your proof, clearly indicate the previous clauses used. If "people like bananas" cannot be proven, then clearly explain or demonstrate why.

d. Using proof by refutation and resolution, try to prove that people like apples using your KB from (b). For each new clause in your proof, clearly indicate the previous clauses used. If "people like apples" cannot be proven, then clearly explain or demonstrate why.