State the converse and contrapositive of each of the following statements: (i) p: A positive integer is prime only if it has no divisors other than 1 and itself. (ii) q: I go to a beach whenever it is a sunny day. (iii) r: If it is hot outside, then you feel thirsty.

Question

Philoid · Accepted Answer

We know that

the converse of a given statement “if p, then q” is if q, then p and the contra positive of the statement if p, then q is “if ∼q, then ∼p”.

(i) The statement p can be rewritten as

If a positive integer is prime, then it has n divisors other than 1 and the number itself.

Converse of statement p is

If a positive integer has no divisors other than 1 and the number itself, then it is prime.

Contra positive of statement p is

If a positive integer has divisors other than 1 and the number itself, then it is not prime.

(ii) The statement q can be rewritten as

If it is a sunny day, then I go to a beach.

Converse of statement q is

If I go to a beach, then it is a sunny day.

Contra positive of statement q is

If don’t go to a beach, it is not a sunny day.

(iii) Converse of statement r is

If you feel thirsty, then it is hot outside.

Contra positive of statement r is

If you don’t feel thirsty, then it is not hot outside.

State the converse and contrapositive of each of the following statements:(i) p: A positive integer is prime only if it has no divisors other than 1 and itself.(ii) q: I go to a beach whenever it is a sunny day.(iii) r: If it is hot outside, then you feel thirsty.

State the converse and contrapositive of each of the following statements:
(i) p: A positive integer is prime only if it has no divisors other than 1 and itself.

(ii) q: I go to a beach whenever it is a sunny day.

(iii) r: If it is hot outside, then you feel thirsty.