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# Chapter 14 - Mathematical Reasoning

In this chapter, you’ll study what Mathematical Reasoning is all about. The ability to ‘reason’ is one of the most essential characteristics of human beings that distinguish them from other species. In NCERT Solutions for Class 11 Maths, Chapter 14, you’ll learn how the power of reasoning, is used in mathematics to prove certain statements and to find whether a statement is true or false. It is interesting to know that there are two kinds of reasoning in mathematics – inductive and deductive. Inductive reasoning is a part of mathematical induction. In this chapter, you will get an idea of what is deductive reasoning.

Mathematical reasoning plays a significant role in our day to day lives. It is a critical skill that helps you to understand mathematics in a better way. Moreover, it also enhances your problem solving and logical skills by developing and explaining solutions and drawing logical conclusions.

## Let’s take a look at topics and sub-topics of Class 11 Maths Chapter 14, Mathematical Reasoning

14.1 Introduction

14.2 Statements

14.3 New Statements from Old

14.4 Special Words/Phrases

14.5 Implications

14.6 Validating Statements

## In Class 11 Maths Chapter 14, you will learn –

Section 14.2 – In this section, you’ll study what is a ‘statement’ in mathematics and how a statement is different from a sentence.

Section 14.3 – In this section, you’ll acquire knowledge about ‘negation of a statement’ and how to write such statements. You’ll also learn what compound statements are and how to find the component statements of the given compound statements.

Section 14.4 – In this section, you’ll study some special words or phrases, which act as connecting words such as ‘and’ and ‘or’. These connecting words (or connectives) are often used in mathematical statements. You’ll also learn about quantifiers such as ‘there exists’, ‘for all’ and how important they are to validate a statement.

Section 14.5 – In this section, you’ll get knowledge about various implications in a mathematical language such as ‘if-then’, ‘only if’ and ‘if and only if’. These kinds of implications are often found in mathematics. You’ll also learn what contrapositive, converse contrapositive and converse statements are.

Section 14.6 – In this section, you’ll learn the techniques and some general rules to validate a statement. You’ll acquire skills how to show whether a statement is true or false by using words and phrases like ‘and, ‘or’, ‘if and only’, ‘if-then’, ‘for every’, ‘there exists’.

In this chapter, you are provided with several examples along with their solutions for a clear understanding of Mathematical Reasoning. To know more about Class 11 Maths Chapter 14 Mathematical Reasoning, you should explore the exercises below. You can also download the Mathematical Reasoning Class 11 NCERT Solutions PDF, solved by expert Maths trainers.

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