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.