Question

Write the contrapositive and converse of the following statements. 

(i) If a number is divisible by 9, then it is divisible by 3 

(ii) If you are born in India, then you are a citizen of India. 

(iii) If a triangle is equilateral, then it is isosceles 

(iv) If x is a prime number, then x is odd 

Answer 1

(i) Let p : A number is divisible by 9 

q : A number is divisible by 3 

Its converse is q ⇒ p and its contrapositive is ~q ⇒~P 

∴ contrapositive: ‘If a number is not divisible by 3, then it is not divisible by 9’. 

Converse: ‘If a number is divisible by 3 then it is divisible by 9. 

(ii) Contrapositive: ‘If you are not a citizen of India then you were not born in India’. 

Converse: ‘If you are a citizen of India then you are born in India’. 

(iii) Contrapositive: ‘If a triangle is not isosceles, then it is not equilateral’. 

Converse: ‘If a triangle is isosceles, then it is equilateral’.

(iv) Contrapositive: ‘If x is not odd, then x is not a prime number’. 

Converse: If x is odd then x is a prime number