NCERT Class XI Mathematics - Mathematical Reasoning - Solutions
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Question : 20
Total: 25
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.
(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:
(i) The contrapositive of the given statement is:
If a positive integer has divisors other than 1 and itself, then it is not prime.
The converse of the given statement is :
If a positive integer has no divisors other than 1 and itself, then it is a prime.
(ii) The contrapositive of the given statement is:
If I do not go to a beach, then it is not a sunny day.
The converse of the given statement is:
If I go to beach, then it is a sunny day.
(iii) The contrapositive of the given statement is:
If you do not feel thirsty, then it is not hot outside.
The converse of the given statement is:
If you feel thirsty, then it is hot outside.
If a positive integer has divisors other than 1 and itself, then it is not prime.
The converse of the given statement is :
If a positive integer has no divisors other than 1 and itself, then it is a prime.
(ii) The contrapositive of the given statement is:
If I do not go to a beach, then it is not a sunny day.
The converse of the given statement is:
If I go to beach, then it is a sunny day.
(iii) The contrapositive of the given statement is:
If you do not feel thirsty, then it is not hot outside.
The converse of the given statement is:
If you feel thirsty, then it is hot outside.
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