Summary of Complement of Set

Introduction to summary of complement set

A universal set is the set of all elements, denoted by the alphabet capital U or occasionally capital E. Set is generally represented by a rectangle and labeled U in Venn diagrams.

Let A be a given set and U be the universal set. The set of all elements of U which are not present in A is called the complement of the set A and is denoted by A' or Ac or A. In this article for Summary of complement set we shall discuss about the  examples for summary of complement set.

Note: Ac = U - A.

Examples on Summary of Complement of Set:

Examples on summary of complement of set are:

The complement of set is one of the operations of the set. Let Set A, the complement of set A represented by A’, is the set of all elements in the set that are not in A.

The shaded area outside A represent complement of A.

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

n(A) + n(A’ ) = n( U ).

Example:

Let U = {x : x is an integer, –4 = x = 6}, Q = {–4, –2, 0, 2, 4, 5} and

R ’ = {–3, –2, –1, 2, 3}.

a) List the elements of set Q’ or complement of  Q

b) Find n(R’)

c) Draw a Venn diagram to the sets U, Q and complement of Q or (Q ’)

Solution:

a) First, list out the members of U.

U = {–4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6}

Q ’ = {–3, –1, 1, 3, 6} ? in U but not in Q

b) Find n(R)

n( U ) = 11, n(R ’ ) = 5

Use the formula:

n(R) + n(R ’ ) = n( U )

n(R) = n( U ) – n(R ’ ) = 11 – 5 = 6

c) Draw a Venn diagram to display the sets U , Q and Q ’

Practice Problems on Summary of Complement of Set:

Practice problem on summary of complement of set are:

1. Let U = {x : x is an integer, –4 = x = 7}, R = {–4, –2, 0, 2, 4, 5, 6} and S’ = {–3, –2, –1, 2, 3}.

a) List the elements of set R’ or complement of  R.

Answer: R’ = {–3, –1, 1, 3, 7}

b) Find n(S)

Answer: 7