# 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. 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 pineapple, 1 banana, 1 apple}

Let U = {1 orange, 1 apricot, 1 pineapple, 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 ## Recent Articles 1. ### Introduction to Physics

Nov 18, 20 01:20 PM

Top-notch introduction to physics. One stop resource to a deep understanding of important concepts in physics

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius! Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.