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Exercise - 14.2

Mathematical Reasoning

**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.

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