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### Set Representation

Three ways to represent a set:

**1. List Representation**

Let us suppose we have a set A with elements 5,8,3,f and w.Generally,a set is represented by listing all the elements of it.Here ,set A is represented by

A={5,8,3,f,w}

**2. Predicate Representation**

In this representation,a set is defined by a predicate.This representation is more convenient than list representation.

*For example*: B={y | y is an even positive integer}Let us suppose Q(y) denoted "y is an even positive integer" then B={y | Q(y) }

If we want to tell some element

*a*belongs to a set A then for this Q(a) has to be true .*For example*:**2 ϵ B**because 2 is an even positive integer.but

**1 ∉ B**because 1 is not an even positive integerThe sets which are usually specified by listing elements can also be specified by predicates

*For example*: A={5,8,3,f,w} is equivalent to{x | (x=5) ∨ (x=8) ∨ (x=3) ∨ (x=f) ∨ (x=w)}

**3. Missing Element Representation**

Sometimes it is convenient to represent sets by missing element representation.

Example : B={y | y is an even positive integer}

B={2,4,6,....}