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Venn Diagrams

Venn Diagrams Online Tutoring / Homework Help
Venn diagram is a diagrammatical representation of sets. A Venn diagram consists of a rectangle where the universal set U, is represented by interior of the rectangle. The other sets are represented by circles or ellipses. The elements or members of a set are written inside the circle.

For example:

The Venn diagram of AJ B (A is subset of B) will be drawn as:



If A and B are two mutually exclusive or disjoint sets then the Venn diagram will be:



Below are a few more examples of Venn diagrams:

  • An example of a Venn diagram to represent set operations (union, intersection and compliment) is given below:

    U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
    A = {3, 4, 5, 7} and B = {1, 2, 4, 7}
    Then A T B = {1, 2, 3, 4, 5, 7} and A B = {4, 7} and A' = U A = {1, 2, 6, 8, 9, 10}

    Hence Venn diagram of the above example will be:

  • Given a set I = {x: 3x 2 < 13, x is a positive integer}. Then draw a Venn diagram to represent the set I.

    Solution:

    First we have to solve the value of x from the given equation,
    3x 2 < 13
    L   3x < 15
    L   x < 5

    Hence I = {1, 2, 3, 4}, so the Venn diagram will be:

  • Draw a Venn diagram of A (B   S   C).

    Solution:


    The shaded portion represents A (B   S   C)

  • Draw a Venn diagram of A   T   (B C).

    Solution:

    First we will draw B C which is:


    B - C


    Now the intersection of A and (B C) will be:


    A   T   (B C)

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