**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 2 is greater than 7.**

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

Solution:

(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.

**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”, which is same as that of second statement. Because if a number is not an irrational number, then it is a rational number. Therefore, the given statements are negations of one another.

(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 that of second statement. Therefore, the given two 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 of ‘Number 3 is prime or it is odd’ are:

a: Number 3 is prime.

b: Number 3 is odd.

Both the statements are true.

(ii) The component statement of the given statement ‘All integers are positive or negative’ are:

a: All integers are positive.

b: All integers are negative.

Both the statements are false.

(iii) The component statement of the given statement ‘100 is divisible by 3, 11 and 5’ are:

a: 100 is divisible by 3.

b: 100 is divisible by 11.

c: 100 is divisible by 5.

The statements, a and b, are false and statement c is true.

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