The Chapter 14 of Class 11 NCERT Mathematics book discusses the basic ideas of Mathematical reasoning and fundamentals of deductive reasoning. Inductive and deductive reasoning are the two primary types of reasoning. Deductive reasoning is a hypothesis of whether a statement is true or false given specified conditions, while inductive reasoning is a generalisation based on observation.
To help students have a better understanding of this chapter, Extramarks provides NCERT Solutions for Class 11 Mathematics Chapter 14. The solutions have answers to all the questions that are listed in the NCERT textbook of Mathematics Class 11, Chapter 14.
NCERT Solutions for Class 11 Mathematics Chapter 14 – Mathematical Reasoning
With a wealth of information available on the Internet, finding the right books and answers can be a difficult endeavour. If you’ve been dealing with the same problem, look no further! Students looking for reliable NCERT Solutions Class 11 Mathematics Chapter 14 can visit the Extramarks website. Extramarks is a one-stop destination for all the learning needs of the student. Chapter 14 of grade 11 Mathematics covers the following topics:
| Unit |
Topic |
| 14.1 |
Introduction |
| 14.2 |
Statements |
| 14.3 |
New Statements from Old |
| 14.3.1 |
Negation of a Statement |
| 14.3.2 |
Compound Statements |
| 14.4 |
Special Words/Phrases |
| 14.4.1 |
The word “And” |
| 14.4.2 |
The word “Or” |
| 14.4.3 |
Quantifiers |
| 14.5 |
Implications |
| 14.5.1 |
Contrapositive and Converse |
| 14.6 |
Validating Statements |
| 14.6.1 |
By Contradiction |
14.1 Introduction
This segment uses pictures to introduce the principles covered in the chapter on Mathematical Reasoning: The process of reasoning, distinct types of reasoning, and the fundamentals of deductive reasoning.
- Mathematical Statement: The Pythagorean Theorem is applicable to any right-angled triangle.
- Reasoning: If triangle ABC is a right triangle, Pythagorean Theorem will be applicable.
14.2 Statements
This section defines mathematical statements and provides instances of mathematically valid statements.
- Mathematical Statement: The product of two negative numbers equals a positive number.
14.3 New Statements from Old
This section discusses how to create new statements from old ones. In this process, a technique is applied.
14.3.1 Negation of a Statement
With a few solved instances, this section discusses the negation of a statement.
For example: Mumbai is a big city.
The negation of this statement would be:
- Mumbai is not a big city.
- It is false that Mumbai is a big city.
14.3.2 Compound Statements
This section discusses compound assertions created by combining words like ‘as’, ‘and’, ‘or’, and so on, as well as solved issues.
For example: 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 the connectives “and,” “or,” and so on.
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 with a background in Mathematics or Statistics may apply for the M.Sc statistics programme.
According to the aforementioned statement, students who have taken both Mathematics and Statistics, as well as individuals who have taken only one of these topics, are eligible to apply for the programme.
14.4.3 Quantifiers
With a few illustrations, this section explores various forms of quantifiers.
For example:
- There is a square with equal sides.
- 5n is an odd number for all natural numbers n.
14.5 Implications
With a few illustrations, this section explores different types of implications.
For example: Connecting a person to a certain crime even if no evidence is found.
14.5.1 Contrapositive and Converse
This section discusses contrapositive and converse assertions with a few illustrations.
For example:
- If you are not an Indian citizen, it will be tough to obtain a passport in India. [contrapositive statement]
- If you have completed all of the exercises in the textbook, you will receive high scores on the exam.
- If you score high marks on the exam, you have completed all of the exercises in the textbook. [converse]
14.6 Validating Statements
This section demonstrates how to validate claims using concrete situations and difficulties.
14.6.1 By Contradiction
This section discusses contradiction, the process of verifying a contradiction, and a counterexample, which is illustrated with a few examples.
In NCERT Books, each chapter is followed by an exercise that students must complete. Students will benefit from the Chapter 14 Class 11 Mathematics NCERT Solutions since they will learn how to answer the questions correctly. Students can also download the solution set for free and use it to study for their board and other competitive exams.
<Download Link for NCERT Solutions for Class 11 Mathematics Chapter 14 – Mathematical Reasoning>
Access NCERT Solutions for Class 11 Mathematics Chapter 14 –Mathematical Reasoning
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NCERT Solutions for Class 11 Mathematics Chapter 14 Mathematical Reasoning – Free Download
CBSE-affiliated schools in the country use the NCERT book as their prescribed textbook. It is advised that students should first study the Class 11 Mathematics NCERT Solutions Chapter 14 and then move on to the reference books in order to do well in their Class 11 examinations.
NCERT Solutions Class 11 Mathematics Chapter 14 Mathematical Reasoning
Extramarks provides a wide selection of study tools that help students prepare better. Solution sets, NCERT books, and past years’ question papers are among the study materials available. There’s a dedicated team of Extramarks professionals that prepares the Chapter 14 Class 11 Mathematics NCERT Solutions.
Class 11 Mathematics Chapter 14 Mathematical Reasoning – Weightage Marks
When it comes to validating propositions, students may find the topic of Mathematical Reasoning to be a little puzzling. As a result, practise is required to develop a clear and exact understanding of this topic. The NCERT Solutions by Extramarks are meticulously developed based on considerable research to provide you an in-depth comprehension of this content. These resources have been purposefully designed to encourage and develop deductive thinking in children. This unit is worth two points in the yearly test. To practise with these solutions, click on the links supplied below.
<Link for Exercise 14.1 Sentences and Statements>
<Link for Exercise 14.2 Simple and Compound Statements>
<Link for Exercise 14.3 Basic Logic Connectives>
<Link for Exercise 14.4 Truth Table for Conjunction, Disjunction>
<Link for Exercise 14.5 Negation and Truth Table>
<Link for Exercise 14.6 Conditional Statements>
<Link for Exercise 14.7 Converse and Contrapositive>
Benefits of Mathematical Reasoning Chapter 14 NCERT Solutions
With the NCERT Solutions for Class 11 Mathematics Chapter 14 provided here as a guide, students can crack challenging questions and master the chapter. The solutions come with additional questions that will aid in a thorough knowledge of the chapter. Students who utilise NCERT solutions as a guide will be able to complete their assignments on time. This will assist students to gain a deeper comprehension of the subjects, resulting in a better performance in exams. Other benefits include:
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