Complement Of A Set

The following diagram shows the complement of a set. Scroll down the page for more examples and solutions on the complement of a set.

 

The complement of set A, denoted by A’ , is the set of all elements in the universal set that are not in A.

 

The number of elements of A and the number of elements of A ’ make up the total number of elements in U .

n(A) + n(A’) = n(U)

Example:
Let U = {x : x is an integer, –4 ≤ x ≤ 7}, P = {–4, –2, 0, 2, 4, 5, 6} and
Q ’ = {–3, –2, –1, 2, 3}.
a) List the elements of set P ’
b) Draw a Venn diagram to display the sets U , P and P ’
c) Find n(Q)

Solution:
a) First, list out the members of U.
U = {–4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6, 7}
P ’ = {–3, –1, 1, 3, 7} ← in U but not in P

b) Draw a Venn diagram to display the sets U , P and P ’

c) Find n(Q)
n( U ) = 12, n(Q ’ ) = 5
Use the formula:
n(Q) + n(Q ’ ) = n( U )
n(Q) = n( U ) – n(Q ’ ) = 12 – 5 = 7

Set Worksheets

Subsets
Distinguish between subsets and proper subsets. Find the number of subsets in a given set.

Complement of a Set
Universal set, complement of a set, and subsets.

Complement and Relative Complement

The complement of a set is the collection of all elements which are not members of that set. Although this operation appears to be straightforward, the way we define “all elements” can significantly change the results.

• Show Video Lesson

Learn what a complement of a set is

• Show Video Lesson

Universal set and absolute complement

• Show Video Lesson

Relative complement or difference between sets

• Show Video Lesson

Check out our most popular games!

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.