Mathematics: Relations Functions Sets: Venn Diagram, Different of Sets and Complement of a Set

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Venn Diagram

  • British mathematician John Venn introduced the concept of diagrams to represent sets. According to him universal set is represented by the interior of a rectangle and other sets are represented by interior of circles.

  • Diagrammatical representation of sets is known as a Venn diagram.

Example:

If and then these sets can be represented as the Venn diagram.

Solution:

Example of Venn diagram

Example of Venn Diagram

Example of Venn diagram

Difference of Sets

Consider the sets

And

A new set having those elements which are in but not in is said to be the difference of sets and and it is denoted by

Similarly, a set of those elements which are in but not in is said to be the difference of and and it is devoted by

In general, if and are two sets then

and

Difference of two sets can be represented using Venn diagram as:

Example of Difference of Sets

Example of Difference of Sets

Example of Difference of Sets

Complement of a Set

Let denote the universal set and its subsets where

is any member of a family

is a male member of the family

is a female member of the family

  • is a set having female members of the family.

  • is a set having male members of the family.

  • is said to be the complement of and is usally denoted by or .

  • is said to be complement of and denoted by or .

Example:

Let be the universal set and its subset where

Find (i) (ii) Represent in Venn diagram.

Solution:

It is given

and

  1. Example of Complement of a Set

    Example of Complement of a Set

    Example of Complement of a Set

Note:

  • Difference of two sets can be found even if none is a subset of the other but complement of a set can be found only when the set is a subset of some universal set.

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