SETS, RELATIONS AND FUNCTIONS

SET A well-defined collection of objects such that given an object, it is possible to determine

whether that object belongs to the given collection or not. For example, the collection of all students of RF Review Center is a set, whereas,

collection of all good books on mathematics is not a set, since a mathematics books on mathematics is not a set, since a mathematics book considered good by one person might be considered bad or average by another.

Two methods of representing a set:A. Roster method (Tabular method)

All elements are listed between two curly brackets and are separated by commas.Ex: A= {2 , 3 , 5, 7, 11, 13, 17, 19 }

B. Rule method (Property method) All the properties which are satisfied by the elements of the set and not by other

elements outside the set are stated.Ex: A= {x|x is a prime number less than 20 }

Set Notations

Notation Meaning

a ∈ A a is an element of A

a ∉ A a is not an element of A

R, R-, R+ the sets of real numbers, negative real numbers, and positive real numbers

Z, Z-, Z+ the sets of all integers, negative integers, positive integers

Q, Q-, Q+ the sets of all rational numbers, negative rational numbers and positive rational numbers

N the set of natural numbers

A ⊆ B A is a subset of B

A ⊈ B A is not a subset of B

∅ null set or empty set