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.

Asked by Pragya Singh | 11 months ago |  102

1 Answer

Solution :-

(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, then 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 don’t 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

Answered by Abhisek | 11 months ago

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