Question

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

Answer 1

(i) Statement $p$ can be written as follows
If a positive integer is prime, then it has no divisors other than $1$ and itself.
The converse of the statement is as follows
If a positive integer has no divisors other than $1$ and itself then it is prime.
The contrapositive of the statement is as follows
If positive integer has divisors other than $1$ and itself it is not prime.
(ii) The given statement can be written as follows
If it is a sunny day then I go to a beach.
The converse of the statement is as follows
If I go to a beach then it is a sunny day.
The contrapositive of the statement is as follows
If I do not go to a beach then it is not a sunny day.
(iii) The converse of statement $r$ is as follows
If you feel thirsty then it is hot outside.
The contrapositive of statement $r$ is as follows
If you do not feel thirsty then it is not hot outside.