Statements and their converses
Let us represent logical statements by capital letters. The statement “If A then B” is a conditional statement involving the statements A and B.
Example: If there is a storm, then the party shall be cancelled.
Converse : If B, then A.
Inverse : If not A, then not B.
Contrapositive : If not B, then not A.
A statement is logically equivalent to its contrapositive. Clearly, the inverse is the contrapositive of the converse.
Sets are well-defined collections of objects. There are three common ways to describe a set. Let us give an example
In words : is the set of natural numbers less than or equal to .
List notation : .
Set builder notation : .
Visual representation by Venn diagrams
Relations and Mapping
Cartesian product of two sets and is defined as . A relation between and is a subset of . If then is said to be related to . We denote this statement by . The relation is said to be a function from to if
(i) Given any , there is a such that .
(ii) and implies that .
The function is said to be
(i) injective if and implies .
(ii) surjective if given any there exists a such that .
(iii) bijective if it is both injective and surjective.