# 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

**Solution:**

The converse of a statement "If A then B" is "If B then A".

The contrapositive of a statement "If A then B" is "If not B then not A".

Accordingly,

**(i)** Statement p can be written in "if-then" format as follows:

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

Then:

- converse: If a positive integer has no divisors other than 1 and itself, then it is prime.
- contrapositive: If positive integer has divisors other than 1 and itself, then it is not prime.

**(ii)** Statement q can be written in "if-then" format as follows:

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

Then

- converse: If I go to a beach, then it is a sunny day.
- contrapositive: If I go do not go to a beach, then it is not a sunny day.

**(iii) **The given statement is:

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

Then

- converse: If you feel thirsty, then it is hot outside.
- contrapositive: If you do not feel thirsty, then it is not hot outside

NCERT Solutions Class 11 Maths Chapter 14 Exercise ME Question 2

## 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

**Summary:**

The following converse and contrapositive statements respectively are

(i) converse: If a positive integer has no divisors other than 1 and itself, then it is prime

contrapositive: If positive integer has divisors other than 1 and itself, then it is not prime

(ii) converse: If I go to a beach, then it is a sunny day

contrapositive: If I go do not go to a beach, then it is not a sunny day

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

contrapositive: If you do not feel thirsty, then it is not hot outside