# Class 11 Maths NCERT Solutions for Chapter 14 Mathematical Reasoning Exercise 14.2

### Mathematical Reasoning Exercise 14.2 Solutions

**1. Write the negation of the following statements:(i) Chennai is the capital of Tamil Nadu.(ii) √2 is not a complex number.(iii) All triangles are not equilateral triangle.(iv) The number 2 is greater than 7.(v) Every natural number is an integer. **

**Solution**

(i) Chennai is not the capital of Tamil Nadu.

(ii) √2 is a complex number.

(iii) All triangles are equilateral triangles.

(iv) The number 2 is not greater than 7.

(v) Every natural number is not an integer.

**2. Are the following pairs of statements negations of each other?(i) The number x is not a rational number.The number x is not an irrational number.(ii) The number x is a rational number.The number x is an irrational number.**

**Solution**

(i) The negation of the first statement is “the number x is a rational number”.

This is same as the second statement. This is because if a number is not an irrational number, then it is a rational number.

Therefore, the given statements are negations of each other.

(ii) The negation of the first statement is “the number x is not a rational number”. This means that the number x is an irrational number, which is the same as the second statement.

Therefore, the given statements are negations of each other.

**3. Find the component statements of the following compound statements and check whether they are true or false.(i) Number 3 is prime or it is odd.(ii) All integers are positive or negative.(iii) 100 is divisible by 3, 11 and 5. **

**Solution**

(i) The component statements are as follows.

p: Number 3 is prime.

q: Number 3 is odd.

Both the statements are true.

(ii) The component statements are as follows.

p: All integers are positive.

q: All integers are negative.

Both the statements are false.

(iii) The component statements are as follows.

p: 100 is divisible by 3.

q: 100 is divisible by 11.

r: 100 is divisible by 5.

Here, the statements, p and q, are false and statement r is true.