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NCERT Class 11 Mathematics Solutions: Chapter 14 – Mathematical Reasoning Exercise 14.2 Part 1
1. Write the negation of the following statements:
(i) Chennai is the capital of Tamil Nadu.
(ii) is not a complex number.
(iii) All triangles are not equilateral triangle.
(iv) The number is greater than .
(v) Every natural number is an integer.
Answer: (i)
Chennai is not the capital of Tamil Nadu.
Answer: (ii)
is a complex number.
Answer: (iii)
All triangles are equilateral triangles
Answer: (iv)
The number is not greater than .
Answer: (v)
Every number is not an integer.
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.
Answer: (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.
So, the given statements are negations of each other.
Answer: (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.