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Question:
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.
Answer:

Given statements are:

(i) p: A positive integer is prime only if it has no divisors other than 1 and itself.

The given statement can be written as:

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

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

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

 

(ii) q: I go to a beach whenever it is a sunny day.

It can also be written as:

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

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

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

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

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

Contrapositive: If you don not feel thirsty, then it is not hot outside.

 

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