The NCERT Solutions For Class 11 Maths Chapter 14 Mathematical Reasoning prepared by subject experts can be studied through this page. A majority of the problems in the textbook exercises are solved in the pdf given below which enables the pupils to put the concepts together for the examination and ace it. NCERT solutions are simple and comprehensible. These solutions enable a class 11 student to understand the concept of Mathematical Reasoning accurately.

## Download PDF of NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning

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

Beneath are the important topics covered in Class 11 Maths Chapter 14 Mathematical Reasoning of NCERT Solutions.

**14.1 Introduction**

This section introduces the concepts covered in the chapter about Mathematical Reasoning using illustrations, the process of reasoning, different kinds of reasoning, fundamentals of deductive reasoning.

**Mathematical Statement: **Pythagorean Theorem holds good for any right-angled triangle.

**Reasoning: **If triangle ABC is a right triangle, it will follow Pythagorean Theorem.

**14.2 Statements**

This section defines a mathematical statement, mathematically acceptable statement with examples.

**Statement**: Men are more intelligent than women.

**Mathematical Statement**: The product of two negative numbers is positive.

**14.3 New statements from old**

This section explains the production of new statements from the old ones. A technique is used in this process.

14.3.1 Negation of a statement

This section covers the negation of a statement with a few solved examples.

Mumbai is a big city.

The negation of this statement would be :

1] Mumbai is not a big city.

2] It is false that Mumbai is a big city.

14.3.2 Compound Statements

This section talks about the compound statements obtained by using words like “and”, “or” etc including solved problems.

There is something wrong with the taste of the food or the vegetables being uncooked.

The above sentence consists of two smaller statements which are as follows:

There is something wrong with the taste of the food.

There is something wrong with the vegetables being uncooked.

**14.4 Special Words / Phrases**

This section defines connectives “and”, “or” etc.

14.4.1 The word “And”

81 is divisible by 3, 9 and 27.

The above statement has 3 small statements.

81 is divisible by 3.

81 is divisible by 9.

81 is divisible by 27.

14.4.2 The word “Or”

A student who has taken mathematics or statistics can apply for the M.Sc statistics programme.

The above statement means that students who have taken both mathematics and statistics can apply for the programme, also the students who have taken only one of these subjects.

14.4.3 Quantifiers

This section discusses different types of quantifiers with few illustrations.

There exists a square whose sides are equal.

For all natural numbers *n*, 5*n* is an odd number.

**14.5 Implications**

This section discusses different types of implications with few illustrations.

Connecting a person to a certain crime even if no evidence is found.

14.5.1 Contrapositive and converse

This section talks about contrapositive and converse statements with a few examples.

If you are not a citizen of India, then it will be difficult to obtain a passport in India. [contrapositive statement]

If you have solved all the exercises in the textbook, then you will get excellent marks in the exam.

If you get excellent marks in the exam, then you have solved all the exercises in the textbook. [converse]

**14.6 Validating Statements**

This section explains the process of validating the statements with specific cases along with problems.

14.6.1 By contradiction

This section contains information about contradiction, method of verifying a contradiction, counterexample explained through a few illustrations.

Read and learn how to solve a Rubik’s Cube with the layer-by-layer method. It can be learned in an hour.

Get detailed solutions for all the questions listed under below exercises:

Exercise 14.1 Solutions : 2 Questions (Short Answers)

Exercise 14.2 Solutions : 3 Questions(Short Answers)

Exercise 14.3 Solutions : 4 Questions(Short Answers)

Exercise 14.4 Solutions : 4 Questions(Short Answers)

Exercise 14.5 Solutions : 5 Questions(Short Answers)

Miscellaneous Exercise Solutions: 7** **Questions (Short Answers)

## A few points on Chapter 14 Mathematical Reasoning

- A mathematically acceptable statement is a sentence which is either true or false.
- The negation of a statement p: If p denotes a statement, then the negation of p is denoted by ∼p.
- A statement is a compound statement if it is made up of two or more smaller statements. The smaller statements are called component statements of the compound statement.
- The words “And”, “Or”, “There exists” and “For every” exist in compound statements.
- The implications are “If ”, “only if ”, “ if and only if ”.

- The contrapositive of a statement p ⇒ q is the statement ∼ q ⇒ ∼p . The converse of a statement p ⇒ q is the statement q ⇒ p. p ⇒ q together with its converse gives p if and only if q.
- The following methods are used to check the validity of statements: (i) direct method (ii) contrapositive method (iii) method of contradiction (iv) using a counterexample.

Basics Maths are covered in these solution modules to help students progress ahead in their area of studies. The NCERT syllabus ensures that the content covered is appropriate for the students to move ahead in their respective streams in the future. A student needs to understand the concept of Mathematical Reasoning as it is the main chunk in the question paper and carries more marks. Before solving real-world applications and problems, the concept has to be learned thoroughly.