Applied Mathematics - Mathematical Reasoning

Mathematical ReasoningMathematically acceptable statementsConnecting words/ phrases - consolidating the understanding of "if and only if (necessary and sufficient) condition", "implies", "and/or", "implied by", "and", "or", "there exists" and their use through variety of examples related to real life and MathematicsValidating the statements involving the connecting words difference between contradiction, converse and contrapositiveSUMMARY1. A mathematically acceptable statement is a sentence which is either true or false. 2.

Explained the terms: - Negation of a statement p: If p denote a statement, then the negation of p is denoted by ∼p. - Compound statements and their related component statements: 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 role of "And", "Or", "There exists" and "For every" in compound statements. - The meaning of implications "If ", "only if ", " if and only if ". 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 - The contrapositive of a statement p ⇒ q is the statement ∼ q ⇒ ∼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.