® 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 .