# NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning

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NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning-

In this chapter, we will discuss some basic concepts of Mathematical Reasoning. In mathematics, there are mainly two kinds of reasoning happen- inductive reasoning and deductive reasoning. There is a total of 18 questions in 5 exercises and for more practice to this topic, 7 questions are given in the miscellaneous exercise. The NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning are prepared by our subject experts. These NCERT solutions help students in their preparation of CBSE class 11 final examination and in the various competitive exams like JEE Main, VITEEE, BITSAT, etc.

According to ARTHENBOT- There are few things which are not capable of mathematical reasoning and when these can not, it is a sign that our knowledge of them is very confused. As we said above that there are mostly two kinds of reasoning happen- inductive and deductive. The inductive reasoning already covered in NCERT chapter-4 Mathematical induction. In NCERT Class 11 Maths Chapter 14 Mathematical Reasoning we will discuss some fundamentals of deductive reasoning. A mathematically acceptable statement is a statement which is either true or false, but not both simultaneously. NCERT Class 11 Maths Chapter 14 Mathematical Reasoning also explains different types of statements like simple statements, compound statements, negation, conditional statement, biconditional statements, conjunction, disjunction, negation etc.

 Basis for comparison Deductive Reasoning Inductive Reasoning Approach Top-down approach Bottom-up approach Based on Truths, facts and rules Trend or Patterns Starting point Premises Conclusion Process Observation > Pattern > Hypothesis > Theory Theory > Hypothesis > Observation > Confirmation Structure Goes from specific statement to general statement Goes from general statement to specific statement

Example-

Which of the following sentences are statements? Give reasons for your answer.

1. There are 35 days in a month.
2. Mathematics is difficult.
3. The sum of 5 and 7 is greater than 10.
4. The square of a number is an even number.

Solution-

1. There are 28 or 29 or 30 or 31 days in a month. The given sentence is false. Hence it is a statement.
2. Mathematics can be difficult for some and easy for others. So it is neither true nor false. Hence it is not a statement.
3. Sum of 5 and 7 = 5 + 7 = 12 > 10. Hence the sentence is true. So it is a statement.
4.  $2^2 = 4$, which is even, and $3^2 = 9$, which is odd. So the square of a number may be even or maybe odd. Hence it is not a statement.

Topics of NCERT Grade 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

The complete Solutions of NCERT Class 11 Mathematics Chapter 14 is provided below:

## NCERT Solutions for Class 11 Mathematics- Chapter-Wise

 Chapter-1 Chapter-2 Chapter-3 Chapter-4 Chapter-5 Chapter-6 Chapter-7 Chapter-8 Chapter-9 Chapter-10 Chapter-11 Chapter-12 Chapter-13 Chapter-15 Chapter-16

## NCERT Solutions for Class 11- Subject wise

 NCERT Solutions for Class 11 Biology NCERT Solutions for Class 11 Maths NCERT Solutions for Class 11 Chemistry NCERT Solutions for Class 11 Physics

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