Table of Contents
Subject specialists have created NCERT Exemplar Solutions for Class 11 Maths Chapter 14:Mathematical Reasoning, which includes thorough solutions for reference. All of the unsolved questions from the textbook’s exercises are answered here. The NCERT Exemplar Solutions for Class 11 provide useful solutions for improving conceptual knowledge and help in entrance examinations like JEE mains and advanced.
The solutions are carefully solved using student-friendly terms while still adhering to the norms that must be followed when solving NCERT Exemplar Solutions for Class 11. Practicing these answers can be incredibly advantageous not only in terms of exams but also in terms of helping Class 11 pupils perform well in upcoming competitive exams.
The approaches for answering have been given special consideration to stay on target while not deviating from the intended answer. Because time is so important in exams, excellent time management when answering questions is essential for getting the best results.
The number of questions given in the exercise of chapter 14 is given below:
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)
NCERT Exemplar Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning
The important topics and sub-topics explained in the NCERT textbook of Class 11 Maths Chapter 14 Mathematical Reasoning are given below.
14.1 Introduction
This section uses pictures to teach the principles presented in the chapter on Mathematical Reasoning, such as the reasoning process, distinct types of reasoning, and the fundamentals of deductive reasoning.
Mathematical Statement: For a right-angled triangle, the Pythagorean Theorem is applicable.
Reasoning: The Pythagorean Theorem will be applied to triangle ABC if it is a right triangle.
14.2 Statements
In this section, a mathematical statement and mathematically acceptable statement are explained with the help of examples.
Statement: Men are more intelligent than women.
Mathematical Statement: The product of two negative numbers is positive.
14.3 New statements from old
In this section, the production of new statements from the old ones is explained. Following are the technique 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
In this section, the compound statements which is obtained by using the words such as “and”, “or” etc with the help of solved problems is explained.
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
In this section, connectives “and”, “or” etc are discussed.
14.4.1 The word “And”
81 is divisible by 3, 9 and 27.
There are 3 small statements in the above statement.
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 program.
The above statement means that students who have taken both mathematics and statistics can apply for the program, also the students who have taken one of the two subjects can apply for the program.
14.4.3 Quantifiers
In this section, different types of quantifiers with the help of illustrations are discussed.
There exists a square whose sides are equal.
For all natural numbers n, 5n is an odd number.
14.5 Implications
In this section, different types of implications with the help of illustrations are discussed.
Connecting a person to a certain crime even if no evidence is found.
14.5.1 Contrapositive and converse
In this section, contrapositive and converse statements with the help of examples are discussed.
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
In this section, the process of validating the statements with specific cases along with solved problems are discussed.
14.6.1 By contradiction
In this section, information about contradiction, method of verifying a contradiction, counterexample along illustrations are explained.
A few points on Chapter 14 Mathematical Reasoning
- A statement that is either true or untrue is mathematically acceptable.
- If any statement is denoted by ‘p’ then the negation of p is denoted by ∼p.
- A compound statement is a statement that is made up of two or more smaller statements. Such that the smaller statements are the component statements of the compound statement.
- In the compound statement, the words “And”, “Or”, “There exists”, and “For every” are present.
- The word “If ”, “only if ”, “ if and only if ” are the implifications.
- The statement ∼ q ⇒ ∼p is the contrapositive of a statement p ⇒ q. And the statement q ⇒ p is the converse of a statement p ⇒ q. p ⇒ q together with its converse gives p if and only if q.
- To examine the validity of statements following steps are required:
(i) direct method
(ii) contrapositive method
(iii) method of contradiction
(iv) using a counterexample.
The NCERT Exemplar Solutions for Class 11 Maths modules offer important mathematical ideas to help students succeed in their studies. The NCERT syllabus guarantees that the knowledge taught is appropriate for students to progress further in their chosen fields. The notion of Mathematical Reasoning must be understood by a student because it is the most important part of the question paper and carries the most marks. The notion must be properly understood before real-world applications and issues can be solved.
Frequently Asked Questions
What is the importance of the concept of Mathematical Reasoning in Chapter 14 of NCERT Exemplar Solutions for Class 11 Maths?
One of the important chapters in the syllabus of Class 11 is Mathematical Reasoning that will help students enhance their reasoning and logical thinking skills. Our experts' solutions assist students in preparing for numerous competitive exams such as JEE Main, JEE Advanced, and yearly exams. These solutions assist students in comprehending fundamental concepts and their applicability in everyday life.
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Question: Write down the main topics of the NCERT Exemplar Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning.
Answer: Following are the topics that are covered in the NCERT Maths Solutions of Class 11 Chapter 14 Mathematical Reasoning:
- Introduction
- Statements
- New statements from old
- Special words / Phrases
- Implications
- Validating Statements.
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