**Question 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 triangles.

**(iv)** The number 2 is greater than 7.

**(v)** Every natural number is an integer.

**Solution:**

**(i)** Negation of statement is: Chennai is not the capital of Tamil Nadu.

**(ii)** Negation of statement is: is a complex number.

**(iii)** Negation of statement is: All triangles are equilateral triangles.

**(iv)** Negation of statement is: The number 2 is not greater than 7.

**(v)** Negation of statement is: Every natural number is not an integer.

**Question 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)** Let p: The number x is not a rational number.

q: The number x is not an irrational number.

Now, ~p: The number x is a rational number.

~q: The number x is an irrational number.

∴ ~p = q and ~q = p

Thus, p and q are negations of each other.

**(ii)** Let p: The number x is a rational number.

q: The number x is an irrational number.

Now, ~p: The number x is not a rational number.

~q: The number x is not an irrational number.

∴ ~p = q and ~q = p

Thus, p and q are negations of each other.

**Question 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:**p: Number 3 is prime

q: Number 3 is odd.

Both the component statements p and q are true.

**(ii) The component statements are:**p: All integers are positive.

q: All integers are negative.

Both the component statements p and q are false.

**(iii) The component statements are:**p: 100 is divisible by 3.

q: 100 is divisible by 11.

r: 100 is divisible by 5.

The component statements p and q are false whereas r is true.