Question-1 :-  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.

(i) Chennai is not the capital of Tamil Nadu.
(ii) √2 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.
   

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.

(i) The negation of the first statement is “the number x is a rational number”.
  This is same as the second statement. This is because if a number is not an irrational number, then it is a rational number.
  Therefore, the given statements are negations of each other.
(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 the second statement.
  Therefore, the given statements 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.

(i) The component statements are as follows.
  p: Number 3 is prime.
  q: Number 3 is odd.
  Both the statements are true.

(ii) The component statements are as follows. 
  p: All integers are positive.
  q: All integers are negative. Both the statements are false.

(iii) The component statements are as follows. 
  p: 100 is divisible by 3.
  q: 100 is divisible by 11. r: 100 is divisible by 5.
  Here, the statements, p and q, are false and statement r is true.