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Compliment Of A Set

Complement of Set Online Tutoring / Homework Help
Let A be a set. Then the compliment of set A is a set of all elements in the universal set which are not in A.

The compliment of set A is denoted by A. Then from the above definition we can write,

A = U A

The Venn diagram for A is given below:
Complement of Set Online Tutoring / Homework Help
The shaded area outside A is the compliment of A ( A).

For example:
If U = {2, 3, 4, 7, 9, 10, 11, 13} and A = {3, 4, 9, 10}

Then

Compliment of A = A = U - A
= {2, 3, 4, 7, 9, 10, 11, 13} {3, 4, 9, 10}
= {2, 7, 11, 13}

The Venn diagram for the above example is:
Complement of Set Online Tutoring / Homework Help
Hence Compliment of A = A = {2, 7, 11, 13} which is the shaded area.


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