Consider the following prolog facts:

takes(tom, ct331).

takes(mary, ct331).

takes(joe, ct331).

takes(tom, ct345).

takes(mary, ct345).

instructs(bob, ct331).

instructs(ann, ct345).

1. Write a prolog rule called teaches that returns true if a given instructor teaches a given student.

2. Write a prolog query that uses the teaches rule to show all students instructed by bob.

3. Write a prolog query that uses the teaches rule to show all instructors that instruct mary.

4. What is the result of the query: teaches(ann, joe). Why is this the case?

5. Write a prolog rule called classmates that returns true if two students take the same course. Demonstrate with suitable queries that this rule works as described.