### Mathematical Reasoning Exercise 02

## Question:

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) No, the two statements are not negations of each other.

(ii) Yes, the two statements are negations of each other.

## Question:

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

## Answer:

(i) Component statement: Number 3 is prime Answer: True

Component statement: Number 3 is odd Answer: True

(ii) Component statement: All integers are positive Answer: False

Component statement: All integers are negative Answer: False

(iii) Component statement: 100 is divisible by 3 Answer: True

Component statement: 100 is divisible by 11 Answer: True

Component statement: 100 is divisible by 5 Answer: True

## Question:

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

## Answer:

(i) Chennai is not the capital of Tamil Nadu (ii) √2 is a complex number (iii) All triangles are equilateral triangle (iv) The number 2 is not greater than 7 (v) Not every natural number is an integer