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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,....}