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

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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