Plus One Maths Notes Chapter 14 Mathematical Reasoning is part of Plus One Maths Notes. Here we have given Kerala Plus One Maths Notes Chapter 14 Mathematical Reasoning.

Board | SCERT, Kerala |

Text Book | NCERT Based |

Class | Plus One |

Subject | Maths Notes |

Chapter | Chapter 14 |

Chapter Name | Mathematical Reasoning |

Category | Plus One Kerala |

## Kerala Plus One Maths Notes Chapter 14 Mathematical Reasoning

**Fundamentals of Deductive Reasoning**

**Mathematical statement:**A mathematically acceptable statement is a sentence which is either true or false but not both simulta-neously.**Truth value of a statement:**The truth (T) or falsity (F) of a statement.**Simple statement:**A statement is said to be simple if it can not be broken down in to two or more sentences.**Negation of a statement:**The denial of a statement is also a statement, called negation of the statement.- If p denotes a statement, then the negation of p (not p) is denoted by ~ p.

**Validity of the negation of the statement:**

p | ~p |

T F | F T |

**Compound Statements**

A statement is a compound statement if it is made up of two or more smaller (simple or component) statements by using any one of the connectives

No | Connectives | Symbol |

1. | and | ∧ |

2. | or | ∨ |

3. | NOT | ~ |

4. | “If…, then”⇒ | ⇒ |

5. | “If and only if’ | ⇔ |

**Implication or conditional statement can be written in the following ways:**

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

**Contrapositive statement:** The contrapositive of a statement “p ⇒ q” is the statement ~q⇒~p

**Converse of a statement:** Converse of a statement p ⇒ q is the statement q ⇒ p

There are statements involving words like ‘or’, ‘and’, ‘there exists’, ‘for all’ (quantifiers) etc.

**Validity of Statements**

A statement is said to be valid or invalid according as it is true or false.

The following table gives the truth values of p ∧ q, p ∨ q, p ⇒ q. p ⇔ q.

p | q | p∧q | p∨q | p⇒q | p⇔q |

T | T | T | T | T | T |

T | F | F | T | F | F |

F | T | F | T | T | F |

F | F | F | F | T | T |

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

- Direct method
- Contrapositive method
- Method of contradiction
- Using a counter example

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