NCERT Solutions
Class 11 Maths
Mathematical Reasoning

Ex.Misc. Q.2
State the converse and contra positive of each of the following statements:
(1) p: A positive integer is prime only if it has no divisors other than 1 and itself.
(2) q: I go to a beach whenever it is a sunny day.
(3) r: If it is hot outside, then you feel thirsty.
(1) 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 contra positive of the statement is as follows:
If positive integer has divisors other than 1 and itself, then it is not prime.
(2) 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 contra positive of the statement is as follows:
If I do not go to a beach, then it is not a sunny day.
(3) The converse of statement r is as follows:
If you feel thirsty, then it is hot outside.
The contra positive of statement r is as follows.
If you do not feel thirsty, then it is not hot outside.