Venn diagrams were introduced by John Venn. They are also sometimes referred to as Euler diagrams.
These diagrams are a pictorial representation of sets often used to understand the unions, intersections, complements etc. of sets.
A universal set is usually represented by a rectangle. The different sets under consideration are depicted by individual circles as shown below:
In the above examples the universal sets are Students, Animals, Real Numbers and Subjects.
Union
The union of two sets A and B is defined as:
A U B = {x ? U | x ? A or x ? B}
This is depicted by the shaded part as follows:
Intersection
The intersection of two sets A and B is defined as:
A ? B = {x ? U | x ? A and x ? B}
This is depicted by the shaded part as follows:
Exercise
Suppose the universal set is U= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Consider the sets A = {1, 2, 4, 5}, B = {4, 5, 7, 8, 10} and C = { 2, 3, 4, 7, 8, 9}.
Show all this information appropriately in a Venn diagram.
Solution:
Verify: 5 is in A and B; 2 is in A and C; 7, 8 are in B and C. Finally 4 is in all the three.
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