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
(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, ………}
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}
3. If U = {1, 2, 3, 4, 5, 6} and A = {2, 3, 4} then U – A = ~ A = A' = {1, 5, 6}.
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:
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
● Sets
● Subset
● Practice Test on Sets and Subsets
● Problems on Operation on Sets
● Practice Test on Operations on Sets
● Venn Diagrams in Different Situations
● Relationship in Sets using Venn Diagram
● Practice Test on Venn Diagrams
8th Grade Math Practice
From Complement of a Set using Venn Diagram to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.