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.
|Text Book||NCERT Based|
|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:
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
|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.
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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