Class 11 - Mathematics
Mathematical Reasoning - Exercise 14.2
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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.
Answer:
(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.
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.
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.
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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.
Answer:
(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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