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In how many ways a set and a function can be represented?
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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 integer

• The 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,....}