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RD Sharma Class 11 Solutions Chapter 31 - Mathematical Reasoning (Ex 31.6) Exercise 31.6 - Free PDF

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Free PDF download of RD Sharma Class 11 Solutions Chapter 31 - Mathematical Reasoning

Free PDF download of RD Sharma Class 11 Solutions Chapter 31 - Mathematical Reasoning Exercise 31.6 solved by Expert Mathematics Teachers on Vedantu. All Chapter 31 - Mathematical Reasoning Ex 31.6 Questions with Solutions for RD Sharma Class 11 Maths to help you to revise the complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams.

In mathematics, there are two types of reasoning: inductive and deductive.

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RD Sharma Class 11 Solutions Chapter 31

Logic:

  • Logical thinking is concerned with the way in which reasoning occurs.

  • In the context of theorem-proof, they provide guidelines for judging the correctness of a particular argument.


Statement (Proposition):

  • Mathematical reasoning begins with a mathematical statement.

  • In mathematics, a statement is mathematically acceptable if it is either true or false, but not both.

  • An aggressive sentence is either true or false, but not both true and false, which is known as a valid statement. If it is not valid, it is known as an invalid statement.

  • A statement is indicated with a small letter. For example, p, q, r p, q,  etc.


Open and Compound Statement

  • An open statement is referred to as a sentence with one or more variables that becomes a statement when specified values are assigned to the variables.

  • If two or more than two simple statements are combined by the use of words such as ‘and’, ‘or’, ‘not’, ‘if’, ‘then’, ‘if and only if ‘, then the resulting statement is called a compound statement.


Elementary Operations of Logic

  • Conjunction

Compound sentences consisting of two simple sentences p and q with connecting conjunction 'and' are called conjunctions of p and q and are written as p*q.

  • Disjunction

A compound sentence that is formed from two simple sentences p and q with connectives 'or' is called a disjunction of p and q, and is represented by p*q.

  • Negation

Changing the truth value of a statement by using words such as 'no' or 'not' is known as negation. A statement p is negated by ¬p


Truth Value and Truth Table:

  • Truth values can be either "true" or "false," which are represented by the symbols T and F, respectively.

  • A truth table is a table of all possible truth values.

  • A compound statement assigns values to the variables. 

  • The number of statements is proportional to the number of rows


Tautology and Contradiction:

  • Tautology is the compound statement that is true for every value of their components.

  • Contradiction (fallacies) are the compound statements which are false for every value of their components.

FAQs on RD Sharma Class 11 Solutions Chapter 31 - Mathematical Reasoning (Ex 31.6) Exercise 31.6 - Free PDF

1. What does Mathematical Reasoning mean?

Mathematical Reasoning includes understanding the mathematically acceptable statement, how to write new statements from old ones with respect to the negation of a statement, compound statement. There are two types of reasoning that you will study in mathematical reasoning, and they are, Inductive reasoning and deductive reasoning. 

2. What is the use of Mathematical Reasoning?

Mathematical reasoning is vital as it helps to create and develop critical thinking and understand Maths in a more comprehensive and meaningful way. The concepts of reasoning not only help the students to have a deeper and wider understanding of the subject but also help in having a wider take on logical statements. This reasoning can be used in conflict resolution. It requires the application of logical thinking to a situation to derive the right problem-solving strategy for a given problem.

3. What are some other resources to understand the chapter Mathematical Reasoning better?

Some other available resources online are streamlined notes, NCERT Solutions, Exemplar Solutions, RS Aggarwal Solutions, RD Sharma Solutions, practice sheets and so much more. These resources can be used in a way to gain an optimum result. For every student appearing for their math exam, these resources are a must.

4. Why should I solve NCERT back exercises?

The NCERT textbooks have various interesting illustrations that make the textbook very interesting to study.

  • After every concept is introduced, there are solved examples that aid in solidifying the concept in a student’s mind.

  • NCERT textbooks give students loads of practice as there is an exercise with different kinds of questions for every section towards the end of the chapter. These exercises are like summaries of the chapter.

  • These books are designed by subject matter experts and academics and are very well researched. 

  • These books are very easy to understand and follow. Each concept is explained in detail and followed with solved examples and exercises.

  • NCERT textbooks adhere to the CBSE curriculum and are prescribed by CBSE themselves.

5. How many exercises are there in Class 11 Maths RD Sharma Chapter - Mathematical Reasoning?

There are a total of 6 exercises in RD Sharma for Class 11 Maths for Chapter - Mathematical Reasoning. These exercises are very well structured, covering all the concepts that you learn in the chapter. The difficulty level of the exercises increases step-by-step. If you find yourself stuck in any of the exercises/questions, you can head to Vedantu and find the solutions on the website absolutely free of cost.