NCERT Solutions for Class 11 Maths Chapter 14 - Mathematical Reasoning

The underlying idea of Mathematical Reasoning concerning Mathematics and what it means has been put forward and discussed in chapter 14 of CBSE class 11th Maths syllabus. In the earlier chapters, students will get to learn inductive reasoning regarding Mathematical Induction. And, here they will be learning about a few fundamentals of deductive reasoning.

The topics that have been introduced in this chapter for class 11 students are statements accepted mathematically. What are the connecting phrases or words, i.e. giving a consolidated understanding of "implies", "implied by", "and/or", "and", "or", "there exists", and "if and only if condition (necessary and sufficient); validate the statements concerning the connecting words, and a few others as well. For students' crystal clarity and easy understandability, a total of 5 exercises plus a miscellaneous exercise has been given at the end of the chapter. Following are the topics discussed in the chapter:

• Introduction

The concept of Mathematical Reasoning is introduced in the introductory part where through the process of reasoning, illustrations, fundamentals of deductive reasoning, and different types of reasoning the chapter has been explained.

• Statements

Defining a mathematical and mathematically acceptable statement is done under this topic.

• New Statements derived from the Old one

Deriving new statements from old ones using a technique, how a negation of a statement is done, and compound statements have been discussed.

• Special words or phrases

The connecting words, such as "and", "or", etc., and the different types of quantifiers are talked about under this topic.

• Implications

The types of implications, like contrapositive and converse statements, have been presented under this topic.

• Validating Statements

The process where mathematical statements are validated for specific cases is studied here.