For each conditional statement, we determine its converse, contrapositive, and inverse:

---

(a) Conditional Statement:

"I come to class whenever there is going to be a quiz."
This can be rewritten as:
If there is going to be a quiz, then I come to class.
Let:

• $P$: There is going to be a quiz.
• $Q$: I come to class.

1. Converse:
   If I come to class, then there is going to be a quiz.
   (If $Q$, then $P$)

2. Inverse:
   If there is not going to be a quiz, then I do not come to class.
   (If $\neg P$, then $\neg Q$)

3. Contrapositive:
   If I do not come to class, then there is not going to be a quiz.
   (If $\neg Q$, then $\neg P$)

---

(b) Conditional Statement:

"A positive integer is a prime only if it has no divisors other than 1 and itself."
This can be rewritten as:
If a positive integer is a prime, then it has no divisors other than 1 and itself.
Let:

• $P$: A positive integer is a prime.
• $Q$: The integer has no divisors other than 1 and itself.

1. Converse:
   If a positive integer has no divisors other than 1 and itself, then it is a prime.
   (If $Q$, then $P$)

2. Inverse:
   If a positive integer is not a prime, then it has divisors other than 1 and itself.
   (If $\neg P$, then $\neg Q$)

3. Contrapositive:
   If a positive integer has divisors other than 1 and itself, then it is not a prime.
   (If $\neg Q$, then $\neg P$)

---

Do you have any questions or want detailed steps?

Here are 5 related questions to explore further:

1. How does one formally verify that the contrapositive of a statement is logically equivalent to the original statement?
2. What is the significance of the converse of a statement in mathematical reasoning?
3. Can you provide examples where the inverse of a statement is true, but the original statement is false?
4. How are conditional statements used in proofs, especially contrapositive reasoning?
5. How do the definitions of prime numbers influence the truth of the given statements?

Tip:

The contrapositive of a statement is always logically equivalent to the original statement, which is a key principle in mathematical proofs.