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NCERT Class 11 Mathematics Solutions: Chapter 14 – Mathematical Reasoning Exercise 14.2 Part 1

Illustration: NCERT Class 11 Mathematics Solutions: Chapter 14 – Mathematical Reasoning Exercise 14.2 Part 1

1. Write the negation of the following statements:

(i) Chennai is the capital of Tamil Nadu.

(ii) is not a complex number.

(iii) All triangles are not equilateral triangle.

(iv) The number is greater than .

(v) Every natural number is an integer.

Answer: (i)

Chennai is not the capital of Tamil Nadu.

Answer: (ii)

is a complex number.

Answer: (iii)

All triangles are equilateral triangles

Answer: (iv)

The number is not greater than .

Answer: (v)

Every 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.

Answer: (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.

So, the given statements are negations of each other.

Answer: (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.