Venn Diagram

​What is Venn Diagram?

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A Venn diagram is used to represent relationships between a collection of objects or sets

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​The above figure is an example of a Venn diagram. The universal set contains natural numbers from 1 to 10, or U= {1,2,3,4,5,6,7,8,9,10}.

​Sets A= {1,3,5,7,9} and B= {6,7,8,9,10} are also given.

​A B

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C 2 4​

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​Notice that the elements 2 and 4 are outside the circles that represent sets A and B. This means that both numbers are not elements of either A or B.

​Set Operations Using Venn Diagrams There are four basic set operations that are best understood using Venn diagrams. These are union, intersection, difference, and complement.

​1. Union (A∪B)

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The union of sets A and B, detenod by A∪B, is the set that contains all the elements in sets A and B as represented by the shaded region below.

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​2. Intersection (A∩B)

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The intersection of sets A and B, denoted by A∩B, is the set that contains all the common elements to sets A and B.​

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3. ​Difference (A−B)

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The difference of sets A and B, denoted by A–B, is the set that contains all elements in A which are not in B.

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​4. Complement (A′)

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The complement of set A, denoted by A′, is the set that contains all elements in the universal set that are not in set A.

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​Key points:

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• A Venn diagram is used to represent relationships between a collection of objects or sets.

• Venn diagrams can also be used to illustrate the four basic set operations: union, intersection, difference, and complement