Kerala State Board New Syllabus Plus One Maths Notes Chapter 14 Mathematical Reasoning.

## Kerala Plus One Maths Notes Chapter 14 Mathematical Reasoning

I. Statement

The basic unit involved in mathematical reasoning is a mathematical sentence.

A sentence is called a mathematically acceptable statement if it is either true or false but not both. Usually denoted by small letters p, q, r, ……..

Denial of a statement is called the negation of the statement. While forming the negation of a statement, phrases like, “It is not the case” or “it is false that” are also used. The negation of a statement p is denoted by ~p.

II. Compound Statement

Many mathematical statements are obtained by combining one or more statements using some connective words like “and”, “or”, etc.

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.

III. Validity of Statement

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