# Compliment Of A Set

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:

A’ = U – A

The Venn diagram for A’ is given below:

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

The Venn diagram for the above example is:

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:

Hence Compliment of A = A’ = {2, 7, 11, 13} which is the shaded area.

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