Write the negation of the following statement:

(i) Chennai is the capital of Tamilnadu.

(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.

Which of the following sentences are statements? Give reasons for your answer?

(i) There are 35 days in a month.

(ii) Mathematics is difficult.

(iii) The sum of 5 and 7 is greater than 10.

(iv) The square of a number is an even number.

(v) The sides of a quadrilateral have equal length.

(vi) Answer this question.

(vii) The product of –1 and 8 is 8.

(viii) The sum of all interior angles of a triangle is 180° .

(ix) Today is a windy day.

(x) All real numbers are complex numbers.

Give three examples of sentences, which are not statements. Give reasons for the answers.

Are the following pairs of statements negations of each other:

(a) The number x is not a rational number. The number x is not an irrational number.

(b) The number x is a rational number. The number x is an irrational number.

Find the component statements of the following compound statements and check whether they are true or false.

(i) The sun shines or it rains.

(ii) All integers are positive or negative.

(iii) 100 is divisible by 3, 11 and 5.