**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**

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.

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