basic mathematics image
 basic mathematics image

Complement of a set


This lesson will explain how to find the complement of a set. We will start with a definition



Definition:

Given a set A, the complement of A is the set of all element in the universal set U, but not in A.

We can write Ac

You can also say complement of A in U

Example #1.


complement-of-a-set-image


Take a close look at the figure above. d and f are in U, but they are not in A.

Therefore Ac = {d, f}

Sometimes, instead of looking at a the Venn Diagrams, it may be easier to write down the elements of both sets

Then, we show in bold the elements that are in U, but not in A

A = { a, b, c}

U = { a, b, c, d, f}


Example #2.


Let B = {1 orange, 1 pinapple, 1 banana, 1 apple}

Let U = {1 orange, 1 apricot, 1 pinapple, 1 banana, 1 mango, 1 apple, 1 kiwifruit }

Again, we show in bold all elements in U, but not in B

Bc = {1 apricot, 1 mango, 1 kiwifruit}


Example #3.


Find the complement of B in U

B = { 1, 2, 4, 6}

U = {1, 2, 4, 6, 7, 8, 9 }

Complement of B in U = { 7, 8, 9}


Example #4.


Find the complement of A in U

A = { x / x is a number bigger than 4 and smaller than 8}

U = { x / x is a positive number smaller than 7}

A = { 5, 6, 7} and U = { 1, 2, 3, 4, 5, 6}

Ac = { 1, 2, 3, 4}

Or Ac = { x / x is a number bigger than 1 and smaller than 5 }

The graph below shows the shaded region for the complement of set A


Complement-of-A-image


This ends the lesson about the complement of a set.








Page copy protected against web site content infringement by Copyscape





worksheets-banner









Copyright © 2008-2015. Basic-mathematics.com. All right reserved

Are you a fan of this site? Support us     Our awards!     Our partners     About me     Disclaimer     Build your website!     Advertise on my site
    Try our free toolbar     Like us on Facebook     Take our survey     Illustrated fractions     Educational math software     Math jobs     Best Teacher Sites Now     Teachers/Students tools     Search math jobs     Algebra ebook     Fraction ebook     Geometric formulas ebook