NCERT Solutions for Exercise 14.3 Class 11 Maths Chapter 14 - Mathematical Reasoning

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

Edited By Safeer PP | Updated on Jul 13, 2022 06:28 PM IST

NCERT solutions for exercise 14.3 Class 11 Maths chapter 14 lists questions related to the usage of “or” and “and” in component statements. Also, questions related to quantifiers are given in exercise 14.3 Class 11 Maths. The types of questions discussed in the NCERT Solutions for Class 11 Maths chapter 14 exercise 14.3 identify the connecting word and braking of the component statement, checking negation and questions related to identifying quantifiers.

Practice questions on inclusive and exclusive or are also there in the NCERRT syllabus Class 11 Maths chapter 14 exercise 14.3. The NCERT Class 11 Maths book chapter mathematical reasoning has the following exercises along with the Class 11th Maths chapter 14 exercise 14.3. All the exercises listed are important and practising these will give a good idea of topics discussed in the chapter.

## Mathematical Reasoning Class 11 Chapter 14-Exercise: 14.3

All rational numbers are real and all real numbers are not complex.

Answer:

The connecting word here is 'and'.

The component statements are:

p: All rational numbers are real.

q: All real numbers are not complex.

Square of an integer is positive or negative.

Answer:

The connecting word here is 'Or'.

The component statements are:

p: Square of an integer is positive.

q: Square of an integer is negative.

The sand heats up quickly in the Sun and does not cool down fast at night.

Answer:

The connecting word here 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.

$x = 2$ and $x = 3$ are the roots of the equation $3x^2 - x - 10 = 0$ .

Answer:

The connecting word here is 'and'.

The component statements are:

p: x = 2 is a root of the equation $3x^2 - x - 10 = 0$ .

q: x = 3 is a root of the equation $3x^2 - x - 10 = 0$ .

There exists a number which is equal to its square.

Answer:

Given, p: There exists a number which is equal to its square.

Quantifier is "There exists".

Negation is, p': There does not exist a number which is equal to its square.

For every real number $x$ , $x$ is less than $x + 1$ .

Answer:

Given, p: For every real number $x$ , $x$ is less than $x + 1$ .

Quantifier is "For Every".

Negation is, p': There exists a real number x such that x is not less than x + 1.

There exists a capital for every state in India.

Answer:

Given, p: There exists a capital for every state in India.

Quantifier is "There exists".

Negation is, p': There does not exist a capital for every state in India. Or, There exists a state in India which does not have a capital.

(i) $x + y = y + x$ is true for every real numbers $x$ and $y$ .
(ii) There exists real numbers $x$ and $y$ for which $x + y = y + x$ .

Answer:

p: $x + y = y + x$ is true for every real numbers $x$ and $y$ .
q: There exists real numbers $x$ and $y$ for which $x + y = y + x$ .

The negation of p is:

There exists no real numbers x and y for which $x + y = y + x$

which is not equal to q.

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

Sun rises or Moon sets.

Answer:

It is not possible for the Sun to rise and the moon to set simultaneously.

Here 'Or' is exclusive

To apply for a driving licence, you should have a ration card or a passport.

Answer:

A person can have both ration card or a passport to apply for a driving license.

Here 'Or' is inclusive.

All integers are positive or negative.

Answer:

All integers are either positive or negative but cannot be both.

Here 'Or' is exclusive.

## More About NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3

There are 4 main questions in the exercise 14.3 Class 11 Maths and 12 questions including the sub-questions. The Class 11 NCERT books will definitely help students in developing their problem-solving skills. The NCERT solutions for Class 11 Maths chapter 14 exercise 14.3 helps in developing problem-solving skills in topics covered in the questions.

Also Read| Mathematical Reasoning Class 11 Notes

## Benefits of NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3

• One of the best ways to understand the concepts in mathematics is to practise questions and exercise 14.3 Class 11 Maths help for the same.

• All questions of Class 11 Maths chapter 14 exercise 14.3 are important from the exam point of view and may get a similar type of questions

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## Subject Wise NCERT Exampler Solutions

### Frequently Asked Question (FAQs)

1. What can you say about a simple statement?

Some statements cannot be broken down into two or more statements. Such statements are known as a simple statement.

2. Compound statements are formed using connectives. Can you list some connectives?

Or, if then, if and only if

3. Give an example of the biconditional connective?

If and only if

4. Give an example of an open statement

Example: He is a college student.

5. How many questions are solved in exercise 14.3 Class 11 Maths?

Four questions and their subquestions are discussed in the NCERT solutions for Class 11 Maths chapter 14 exercise 14.3

6. When can you say that a compound statement with and is true?

If all the component statements of the given compound statement are true.

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