Q.State the converse and contrapositive of each of the following statements:

1. p: "A positive integer is prime only if it has no divisors other than 1 and itself" (i.e., "If a positive integer is prime, then it has no divisors other than 1 and itself"). Converse: "If a positive integer has no divisors other than 1 and itself, then it is prime." Contrapositive: "If a positive integer has a divisor other than 1 and itself, then it is not prime."
2. q: "I go to a beach whenever it is a sunny day" (i.e., "If it is a sunny day, then I go to a beach"). Converse: "If I go to a beach, then it is a sunny day." Contrapositive: "If I do not go to a beach, then it is not a sunny day."
3. r: "If it is hot outside, then you feel thirsty." …

First convert to clean "if p then q" form (watch for "only if" and "whenever", both of which signal p ⇒ q). Convers …

• Misreading "prime only if no other divisors" — "p only if q" means p ⇒ q, not q ⇒ p. …