Set Operations

In math, set theory is used to learn about the sets. It is a group of things. It contains many operations like union, intersection, complement and power set. Set theory has the lot of symbols. Union is the combination of two sets. Union represents by the ‘∪’ symbol. Intersection is the common values of two sets. Intersection represents the ‘∩’ symbol. We can join the numbers of sets by using this method. Number of laws is used in set theory.

Venn diagrams

Venn diagrams are the logical relations between groups of sets. We can draw the venn diagrams with the help of three or four circles. Here also we can use the union, intersection and complement operations. Now we will see the example problems for set operations and venn diagrams.

Example for Set Operation

A={8,12,15,18,21} B={8,12,17,19,20} C={5,12,17,23,35}. Find the (A∪B)∩C.

Solution:

The given sets are  A={8,12,15,18,21} B={8,12,17,19,20} C={5,12,17,23,35}.

Now we can find the (A∪B)∩C. First find the A∪B.

A∪B

It is a combination of A and B sets. So group the values of A and B sets.

A∪B = {8,12,15,17,18,19,20,21}

(A∪B)∩C

Now select the common values from A∪B  and C sets.

So (A∪B)∩C={12,17}.

Example for Venn Diagram

There are 40 students are in the school. In those students, 16 students are passed in English and 15 students are passed in Maths. Draw the Venn diagram for this information and find how many students passed in both English and Maths.

Solution:

First list out the given information.

Total number of students=40

Number of students passed in English=16

Number of students passed in Maths =15

Now draw the diagram for this information.

Venn Diagram for Two Sets

First add the English and Maths passed out students=16+15

=31.

Now subtract 31 students from the total number of students.

So number of students passed in both English and Maths =40-31

=9.


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Result for Two Sets Venn Diagram

Therefore 9 students are passed in both English and Maths.

The above example problems are used to study the set operations and venn diagrams.