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

You can also say complement of A in U

Therefore A

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,

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

Let U = {1 orange,

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

B

Find the complement of B in U

B = { 1, 2, 4, 6}

U = {1, 2, 4, 6,

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

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}

A

Or A

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