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## CBSE Guide Mathematical Reasoning class 11 Notes

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## Mathematical Reasoning class 11 Notes Mathematics

Download CBSE class 11th revision notes for Chapter 14 Mathematical Reasoning class 11 Notes Mathematics in PDF format for free. Download revision notes for Mathematical Reasoning class 11 Notes Mathematics and score high in exams. These are the Mathematical Reasoning class 11 Notes Mathematics prepared by team of expert teachers. The revision notes help you revise the whole chapter in minutes. Revising notes in exam days is on of the best tips recommended by teachers during exam days.

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**CBSE Class 11 Mathematics Revision Notes Chapter-14 Mathematical Reasoning class 11 Notes Mathematics**

**1. Statements: **A statement is a sentence which either true or false, but not both simultaneously.

For example: “A triangle has a four sides.”, “New Delhi is the capital of India.” are the statements.

**2. Negaiton of a statement**: Negation of a statement p: If p denote a statement, then the negation of p is denoted by ∼p.

**3. Compound statement**: A statement is a compound statement if it is made up of two or more smaller statements. The smaller statements are called component statements of the compound statement.

The Compound statements are made by:

(i) **Connectives**: “AND”, “OR”

(ii) **Quantifiers**: “There exists”, “For every”

(iii) **Implications:** The meaning of implications “If ”, “only if ”, “ if and only if ”.

(a) “p

q is necessary condition for p.

The converse of a statement p ⇒ q is the statement q ⇒ p.

p⇒ q together with its converse, gives p if and only if q.

(b) “p

A sentence with if p, then q can be written in the following ways.

- p implies q (denoted by p ⇒ q)
- p is a sufficient condition for q
- q is a necessary condition for p
- p only if q
- ∼q implies ∼p

**4. Contrapositive**: The contrapositive of a statement p ⇒ q is the statement ∼ q ⇒∼p .

**New statements, Special words/phrases**

**5. Contradiction : **If to check whether p is true we assume negation p is true.

**6. Validating statements**: Checking of a statement whether it is true or false. The validity of a statement depends upon which of the special.

- The following methods are used to check the validity of statements:

(i) direct method

(ii) contrapositive method

(iii) method of contradiction

(iv) using a counter example.

## Mathematical Reasoning class 11 Notes

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