Complement of a Set using Venn Diagram

The complement of a set using Venn diagram is a subset of U. Let U be the universal set and let A be a set such that A ⊂ U. Then, the complement of A with respect to U is denoted by A' or A\(^{C}\) or U – A or ~ A and is defined the set of all those elements of U which are not in A.

Thus, A' = {x ∈ U : x ∉ A}.

Clearly, x ∈ A' ⇒ x ∉ A

Complement of a Set using Venn Diagram

(A – B) is also called the complement of B relative to A. From the definition it is clear that the complement of the whole set in a set is the null set; for U' = U – U = ∅ again ∅' = U - ∅ = U also (A')' = U – A' = U – (U – A) = A. If the set of real numbers be the universal set, then the set of rational numbers and the set of irrational numbers are complements of each other. 

Example on complement of a set using Venn diagram:

1. Let the set of natural numbers N = {1, 2, 3, ………..} be the universal set and let A = {2, 4, 6, 8, ……….}

Then A' = {1, 3, 5, ………}

Complement of a Set Venn Diagram

2. If U = {1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {1, 3, 5, 7, 9} then A' = {2, 4, 6, 8}

Complement of a Set

3. If U = {1, 2, 3, 4, 5, 6} and A = {2, 3, 4} then U – A = ~ A = A' = {1, 5, 6}.

Example on Complement of a Set

4. U = {1, 2, 3, 4, 5, 6} be the universal set and A = {1, 3, 5} then A' = {2, 4, 6}.

Properties of Complement of a Set

Properties of complement of a set:

1. U' = ∅

2. ∅' = U

3. A U A' = U        For any subset A

4. A ∩ A' = ∅        For any subset A

5. (A')' = A          For any subset A.

Set Theory


Representation of a Set

Types of Sets

Pairs of Sets


Practice Test on Sets and Subsets

Complement of a Set

Problems on Operation on Sets

Operations on Sets

Practice Test on Operations on Sets

Word Problems on Sets

Venn Diagrams

Venn Diagrams in Different Situations

Relationship in Sets using Venn Diagram

Examples on Venn Diagram

Practice Test on Venn Diagrams

Cardinal Properties of Sets

7th Grade Math Problems

8th Grade Math Practice

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