NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.3

# NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.3

## NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.3

NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.3 are the part of NCERT Solutions for Class 11 Maths. Here you can find the NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.3.

### Ex 14.3 Class 11 Maths Question 1.

For each of the following compound statements first identify the connecting words and then break it into component statements.
(i) All rational numbers are real and all real numbers are not complex.
(ii) Square of an integer is positive or negative.
(iii) The sand heats up quickly in the Sun and does not cool down fast at night.
(iv) x = 2 and x = 3 are the roots of the equation 3x2 – x – 10 = 0.

Solution:
(i) The connecting word for the compound statement is ‘and’. The component statements are:
p: All rational numbers are real.
q: All real numbers are not complex.

(ii) The connecting word for the compound statement is ‘or’. The component statements are:
p: Square of an integer is positive.
q: Square of an integer is negative.

(iii) The connecting word for the compound statement is ‘and’. The component statements are:
p: The sand heats up quickly in the Sun.
q: The sand does not cool down fast at night.

(iv) The connecting word for the compound statement is ‘and’. The component statements are:
p: x = 2 is a root of the equation 3x2 – x – 10 = 0.
q: x = 3 is a root of the equation 3x2 – x – 10 = 0.

### Ex 14.3 Class 11 Maths Question 2.

Identify the quantifier in the following statements and write the negation of the statements.
(i) There exists a number which is equal to its square.
(ii) For every real number x, x is less than x + 1.
(iii) There exists a capital for every state in India.

Solution:
(i) Here, the quantifier is ‘there exists’.
The negation of the statement is: There does not exist a number which is equal to its square.
(ii) Here, the quantifier is ‘for every’.
The negation of the statement is: For at least one real number x, x is not less than x + 1.
(iii) Here, the quantifier is ‘there exists’.
The negation of the statement is: There exists a state in India which does not have a capital.

### Ex 14.3 Class 11 Maths Question 3.

Check whether the following pair of statements are negation of each other. Give reasons for your answer.
(i) x + y = y + x is true for every real numbers x and y.
(ii) There exists real numbers x and y for which x + y = y + x.

Solution:
Let p: x + y = y + x is true for every real numbers x and y.
q: There exists real numbers x and y for which x + y = y + x.
Now, ~p: There exists real numbers x and y for which x + y ≠ y + x.
Thus, ~p ≠ q.

Hence, the given statements are not negation of each other.

### Ex 14.3 Class 11 Maths Question 4.

State whether the “Or” used in the following statements is “exclusive” or “inclusive”. Give reasons for your answer.
(i) Sun rises or Moon sets.
(ii) To apply for a driving license, you should have a ration card or a passport.
(iii) All integers are positive or negative.

Solution:
(i) The “Or” used in the given statement is “exclusive”. Since when sun rises, moon does not set during day-time.
(ii) The “Or” used in the given statement is “inclusive”. Since you can apply for a driving license even if you have a ration card as well as a passport.
(iii) The “Or” used in the given statement is “exclusive”. Since an integer is either positive or negative, it cannot be both.

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