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.

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.

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.

For each of the following compound statements first identify the connecting words and then break it into component statements.

(i) All rational numbers are real and all real numbers are not complex.

(ii) Square of an integer is positive or negative.

(iii) The sand heats up quickly in the sun and does not cool down fast at night.

(iv) x = 2 and x = 3 are the roots of the equation 3x² – x – 10 = 0.

Identify the quantifier in the following statements and write the negation of the statements.

(i) There exists a number which is equal to its square.

(ii) For every real number x, x is less then x + 1.

(iii) There exists a capital for every state in India.