Question

State the converse and contrapositive of each of the following statements:
(i) If it is hot outside, then you feel thirsty.
(ii) I go to a beach whenever it is a sunny day.
(iii) A positive integer is prime only if it has no divisors other than 1 and itself.
(iv) If you live in Delhi, then you have winter clothes.
(v) If a quadrilateral is a parallelogram, then its diagonals bisect each other.

Answer 1

(i) Converse of the given statement:
If you feel thirsty, then it is hot outside.
Contrapositive of the given statement:
If you do not feel thirsty, then it is not hot outside.

(ii) Converse of the given statement:
If I go to a beach, then it is a sunny day.
Contrapositive of the given statement:
If I do not go to a beach, then it is not a sunny day.

(iii) Converse of the given statement:
If a positive integer has no divisors other than 1 and itself, then it is prime.
Contrapositive of the given statement:
If a positive integer has some divisors other than 1 and itself, then it is not prime.

(iv) Converse of the given statement:
If you have winter clothes, then you live in Delhi.
Contrapositive of the given statement:
​If you do not have winter clothes, then you do not live in Delhi.

(v) Converse of the given statement:
If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Contrapositive of the given statement:
If the diagonals of a quadrilateral do not bisect each other, then it is not a parallelogram.