Processing math: 100%

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 AC 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

Sets

Representation of a Set

Types of Sets

Pairs of Sets

Subset

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

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.




Share this page: What’s this?

Recent Articles

  1. Converting Fractions to Decimals | Solved Examples | Free Worksheet

    Apr 28, 25 01:43 AM

    Converting Fractions to Decimals
    In converting fractions to decimals, we know that decimals are fractions with denominators 10, 100, 1000 etc. In order to convert other fractions into decimals, we follow the following steps:

    Read More

  2. Expanded Form of a Number | Writing Numbers in Expanded Form | Values

    Apr 27, 25 10:13 AM

    Expanded Form of a Number
    We know that the number written as sum of the place-values of its digits is called the expanded form of a number. In expanded form of a number, the number is shown according to the place values of its…

    Read More

  3. Converting Decimals to Fractions | Solved Examples | Free Worksheet

    Apr 26, 25 04:56 PM

    Converting Decimals to Fractions
    In converting decimals to fractions, we know that a decimal can always be converted into a fraction by using the following steps: Step I: Obtain the decimal. Step II: Remove the decimal points from th…

    Read More

  4. Worksheet on Decimal Numbers | Decimals Number Concepts | Answers

    Apr 26, 25 03:48 PM

    Worksheet on Decimal Numbers
    Practice different types of math questions given in the worksheet on decimal numbers, these math problems will help the students to review decimals number concepts.

    Read More

  5. Multiplication Table of 4 |Read and Write the Table of 4|4 Times Table

    Apr 26, 25 01:00 PM

    Multiplication Table of Four
    Repeated addition by 4’s means the multiplication table of 4. (i) When 5 candle-stands having four candles each. By repeated addition we can show 4 + 4 + 4 + 4 + 4 = 20 Then, four 5 times

    Read More