# CBSE Class 11 Mathematics Mathematical Reasoning Notes

Download CBSE Class 11 Mathematics Mathematical Reasoning Notes in PDF format. All Revision notes for Class 11 Mathematics have been designed as per the latest syllabus and updated chapters given in your textbook for Mathematics in Class 11. Our teachers have designed these concept notes for the benefit of Class 11 students. You should use these chapter wise notes for revision on daily basis. These study notes can also be used for learning each chapter and its important and difficult topics or revision just before your exams to help you get better scores in upcoming examinations, You can also use Printable notes for Class 11 Mathematics for faster revision of difficult topics and get higher rank. After reading these notes also refer to MCQ questions for Class 11 Mathematics given on studiestoday

## Revision Notes for Class 11 Mathematics Chapter 14 Mathematical Reasoning

Class 11 Mathematics students should refer to the following concepts and notes for Chapter 14 Mathematical Reasoning in Class 11. These exam notes for Class 11 Mathematics will be very useful for upcoming class tests and examinations and help you to score good marks

### Chapter 14 Mathematical Reasoning Notes Class 11 Mathematics

Class XI

Chapter:14 Mathematical Reasoning

Chapter Notes

Key Concepts

1. There are two types of reasoning the deductive and inductive. Deductive reasoning was developed by Aristotle, Thales, Pythagoras in the classical Period (600 to 300 B.C.).

2. In deduction, given a statement to be proven, often called a conjecture or a theorem, valid deductive steps are derived and a proof may or may not be established. Deduction is the application of a general case to a particular case.

3. Inductive reasoning depends on working with each case, and developing a conjecture by observing incidence till each and every case is observed.

4. Deductive approach is known as the top-down" approach”. Given the theorem which is narrowed down to specific hypotheses then to observation. Finally the hypotheses is tested with specific data to get the confirmation (or not) of original theory.

5. Mathematical reasoning is based on deductive reasoning. The classic example of deductive reasoning, given by Aristotle, is
· All men are mortal.
· Socrates is a man.
· Socrates is mortal.6. The basic unit involved in reasoning is mathematical statement.

7. A sentence is called a mathematically acceptable statement if it is either true or false but not both. A sentence which is both true and false simultaneously is called a paradox.

8. Sentences which involve tomorrow, yesterday, here, there etc i.e variables etc are not statements.

9. The sentence expresses a request, a command or is simply a question are not statements.

10.The denial of a statement is called the negation of the statement.

11.Two or more statements joined by words like “and” “or” are called Compound statements. Each statement is called a component statement. “and” “or” are connecting words.

12.An “ And” statement is true if each of the component statement is true and it is false even if one component statement is false.

13.An “OR” statement is will be true when even one of its components is true and is false only when all its components are false

14.The word “OR” can be used in two ways (i) Inclusive OR (ii) Exclusive OR. If only one of the two options is possible then the OR used is Exclusive OR. If any one of the two options or both the options are possible then the OR used is Inclusive OR.

15.There exists “\$” and “For all” " are called quantifiers.

16.A statement with quantifier “There exists” is true, if it is true for at least one case.

17.If p and q are two statements then a statement of the form 'If p then q' is known as a conditional statement. In symbolic form p implies q is denoted by p Þ q.

18.The conditional statement p Þ q can be expressed in the various other forms:

(i) q if p (ii) p only if q (iii) p is sufficient for q (iv) q is necessary for p.

19. A statement formed by the combination of two statements of the form if p then q and if q then p is p if and only if q. It is called conditional statement.

20. Contrapositive and converse can be obtained by a if then statement
The contrapositive of a statement p ⇒ q is the statement - q ⇒ -p
The converse of a statement p ⇒ q is the statement q ⇒ p

21. Truth values of various statement

22. Two prove the truth of an if p- then q statement . there are two ways : the first is assume p is true and prove q is true. This is called the direct method.
Or assume that q is false and prove p is false. This is called the Contrapositive method.

23. To prove the truth of “ p if and only if q” statement , we must prove two things , one that the truth of p implies the truth of q and the second that the truth of q implies the truth of p.

24. The following methods are used to check the validity of statements:
(i) Direct method
(ii) Contra positive method
(iv) Using a counter example
25. To check whether a statement p is true , we assume that it is not true, i.e. ∼p is true . Then we arrive at some result which contradicts our assumption.

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### CBSE Class 11 Mathematics Chapter 14 Mathematical Reasoning Notes

We hope you liked the above notes for topic Chapter 14 Mathematical Reasoning which has been designed as per the latest syllabus for Class 11 Mathematics released by CBSE. Students of Class 11 should download and practice the above notes for Class 11 Mathematics regularly. All revision notes have been designed for Mathematics by referring to the most important topics which the students should learn to get better marks in examinations. Studiestoday is the best website for Class 11 students to download all latest study material.

### Notes for Mathematics CBSE Class 11 Chapter 14 Mathematical Reasoning

Our team of expert teachers have referred to the NCERT book for Class 11 Mathematics to design the Mathematics Class 11 notes. If you read the concepts and revision notes for one chapter daily, students will get higher marks in Class 11 exams this year. Daily revision of Mathematics course notes and related study material will help you to have a better understanding of all concepts and also clear all your doubts. You can download all Revision notes for Class 11 Mathematics also from www.studiestoday.com absolutely free of cost in Pdf format. After reading the notes which have been developed as per the latest books also refer to the NCERT solutions for Class 11 Mathematics provided by our teachers

#### Chapter 14 Mathematical Reasoning Notes for Mathematics CBSE Class 11

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#### Chapter 14 Mathematical Reasoning CBSE Class 11 Mathematics Notes

Regular notes reading helps to build a more comprehensive understanding of Chapter 14 Mathematical Reasoning concepts. notes play a crucial role in understanding Chapter 14 Mathematical Reasoning in CBSE Class 11. Students can download all the notes, worksheets, assignments, and practice papers of the same chapter in Class 11 Mathematics in Pdf format. You can print them or read them online on your computer or mobile.

#### Notes for CBSE Mathematics Class 11 Chapter 14 Mathematical Reasoning

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