# Write the contrapositive and converse of the following statements.

(i) If x is a prime number, then x is odd.

(ii) If the two lines are parallel, then they do not intersect in the same plane.

(iii) Something is cold implies that it has low temperature.

(iv) You cannot comprehend geometry if you do not know how to reason deductively.

(v) x is an even number implies that x is divisible by 4.

**Solution:**

We know that

- The contrapositive of a statement "If A then B" is "If not B then not A".
- The converse of a statement "If A then B" is "If B then A".

Accordingly,

**(i)** Contrapositive: If a number x is not odd, then x is not a prime number.

Converse: If a number x is odd, then it is a prime number.

**(ii)** Contrapositive: If two lines intersect in the same plane, then they are not parallel.

Converse: If two lines do not intersect in the same plane, then they are parallel.

**(iii)** Contrapositive: If something is not at low temperature, then it is not cold.

Converse: If something is at low temperature, then it is cold.

**(iv)** Contrapositive: If you know how to reason deductively, then you can comprehend geometry.

Converse: If you do not know how to reason deductively, then you cannot comprehend geometry.

**(v)** Contrapositive: If x is not divisible by 4, then x is not an even number.

Converse: If x is divisible by 4, then x is an even number

NCERT Solutions Class 11 Maths Chapter 14 Exercise 14.4 Question 2

## Write the contrapositive and converse of the following statements. (i) If x is a prime number, then x is odd. (ii) If the two lines are parallel, then they do not intersect in the same plane. (iii) Something is cold implies that it has low temperature. (iv) You cannot comprehend geometry if you do not know how to reason deductively. (v) x is an even number implies that x is divisible by 4

**Summary:**

The following contrapositive and converse statements are (i) If a number x is not odd, then x is not a prime number and If a number x is odd, then it is a prime number.

(ii) If two lines intersect in the same plane, then they are not parallel and If two lines do not intersect in the same plane, then they are parallel.

(iii) If something is not at low temperature, then it is not cold and If something is at low temperature, then it is cold.

(iv) If you know how to reason deductively, then you can comprehend geometry and If you do not know how to reason deductively, then you cannot comprehend geometry.

(v) If x is not divisible by 4, then x is not an even number and If x is divisible by 4, then x is an even number.

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