Venn Diagram of 3 sets

How to Use Venn Diagram to Find the Relation of Sets

A Venn diagram is diagram that shows possible logical relations between finite collection of different sets. The most common Venn diagram contains 2 sets or 3 sets.

Venn diagram of 2 sets

In Venn diagram of 2 sets A,B,C there are 22=4 areas. Each area in the Venn diagram represents a distinct possible logical relation of an item x to one of the 2 sets A,B:

  • x only belongs to A, x does not belong to B
  • x only belongs to B, x does not belong to A
  • x belongs to all 2 sets : A,B
  • x does not any set.

Venn diagram of 3 sets

In Venn diagram of 3 sets A,B,C there are 23=8 areas. Each area in the Venn diagram represents a distinct possible logical relation of an item x to one of the 3 sets A,B,C:

  • x only belongs to A, x does not belong to B and C
  • x only belongs to B, x does not belong to A and C
  • x only belongs to C, x does not belong to A and B
  • x only belongs to two sets : A,B , x does not belong to C
  • x only belongs to two sets : B,C , x does not belong to A
  • x only belongs to two sets : A,C , x does not belong to B
  • x belongs to all 3 sets : A,B.C
  • x does not any set.

Find the Relation of Sets with Venn Diagram

In the next movie, we see how can we use Venn diagram to find the relation of sets.
For example, Suppose we have 2 sets A and B, with Venn diagram we can find:

  • Whether the A is equal to B
  • Whether the A is superset of B
  • Whether the A is subset of B
  • None of the above (In other words A is not equal to B, A is not superset of B and A is not subset of B).

As we can see in the movie, we represent each set in distinct Venn diagram.
Now, when the 2 Venn Diagram are displayed side by side, you can easily see the relation between the sets.

Author: bigsigma

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