Chapter 14: Mathematical Reasoning Exercise 14.2

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

(ii)
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.

(i) The negation of the first statement is ‘the number x is a rational number’.

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

Hence, 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.

Hence, the given statements are negations of each other.

(i) The component statements are

(a) Number 3 is prime.

(b) Number 3 is odd.

Here, both statements are true.

(ii) The component statements are

(a) All integers are positive.

(b) All integers are negative.

Here, both statements are false.

(iii) The component statements are

(a) 100 is divisible by 3.

(b) 100 is divisible by 11.

(c) 100 is divisible by 5.

Here, the statements (a) and (b) are false, and (c) is true.