Let’s learn about Sets before diving deep into the article Complement of a Set. Check out the Definition of Complement of a Set, its Representation, Venn Diagram of the Complement of the Set. Refer to Solved Examples for finding the Complement of a Set. To learn more about the Operations of Sets you can have a look at the Set Theory and clarify all your concerns easily.
Sets Definition
A Well Defined Collection of Objects or Elements is called Sets. Any set containing all the objects or elements related to a particular context is known as a Universal Set and is represented by U.
For any Set A that is a subset of the Universal Set U, the Complement of the Set A contains the elements that are members of Universal Set but not from Set A. The Complement of Set A is denoted by A′.
Complement of a Set
If U is a Universal Set and A is a Subset of U then the Complement of A is the set of all the elements in the Universal Set but not aren’t elements of Set A.
A′ = {x : x ∈ U and x ∉ A}
In Other Words, we can say that the Complement of A is nothing but the difference between the Universal Set and the Sub Set A.
Venn Diagram for Complement of a Set
The Venn Diagram representing the Complement of a Set is given by
Solved Examples on Complement of a Set
1. Let U be a Universal Set that consists of natural numbers greater than 10 and less than 20. A, B are Subsets of U and given by
A ={x:x ∈ U and x is a perfect square}
B = {8, 9, 11, 12, 13}
Find the complement of sets A and B?
Solution:
U = {11,12,13,14,15,16,17,18,19}
A = {x:x ∈ U and x is a perfect square}
= {16}
B = {8, 9, 11, 12, 13}
A′ = U – A
{11,12,13,14,15,16,17,18,19} – {16}
= { 11, 12, 13, 14, 15, 17, 18, 19}
B′ = U – B
= {11,12,13,14,15,16,17,18,19} – {8, 9, 11, 12, 13}
= { 12, 14, 15, 16, 17, 18, 19}
2. If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = { 1, 3, 5, 7}. Find the Complement of A?
Solution:
Given U = {1, 2, 3, 4, 5, 6, 7, 8,, 9, 10}
A = {1, 3, 5, 7}
A′ = U – A
= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} – {1, 3, 5, 7}
= { 2, 4, 6, 8, 9, 10}
3. If U = {3, 5, 7, 9, 11, 13, 15, 17, 19}, A = {6, 10, 4, 16}. Find the Complement of A?
Solution:
U = {3, 5, 7, 9, 11, 13, 15, 17, 19}
A = {6, 10, 4, 16}
A′ = U – A
= {3, 5, 7, 9, 11, 13, 15, 17, 19} – {6, 10, 4, 16}
= {3, 5, 7, 9, 11, 13, 15, 17, 19}