Properties of Elements in Sets

The following properties of elements in sets are discussed here.

If U be the universal set and A, B and C are any three finite sets then;

1. If A and B are any two finite sets then n(A - B) = n(A) – n(A ∩ B) i.e. n(A – B) + n(A ∩ B)  = n(A)

2. If A and B are any two finite sets then n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

3. If A and B are any two finite sets then n(A ∪ B) = n(A) + n(B) ⇔ A, B are disjoint non-void sets.

4. If A and B are any two finite sets then n(A ∆ B) = Number of elements which belongs to exactly one of A or B

                   = n((A – B) ∪ (B – A))

                   = (A – B) + n(B – A) [Since (A - B) and (B – A) are disjoint.]

                   = n(A) – n(A ∩ B) + n(B) – n(A ∩ B)

                   = n(A) + n(B) – 2n(A ∩ B)


Some more properties of elements in sets using three finite sets:

5. If A, B and C are any three finite sets then n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(A – C) + n(A ∩ B ∩ C)


6. If A, B and C are any three finite sets then Number of elements in exactly one of the sets A, B, C = n(A) + n(B) + n(C) – 2n(A ∩ B) – 2n(B ∩ C) – 2n(A – C) + 3n(A ∩ B ∩ C)


7. If A, B and C are any three finite sets then Number of elements in exactly two of the sets A, B, C = n(A ∩ B) + n(B ∩ C) + n(C ∩ A) – 3n(A ∩ B ∩ C)


8. If U be the universal set and A and B are any two finite sets then n(A' ∩ B') = n((A ∪ B)') = n(U) -  n(A ∪ B)


9. If U be the universal set and A and B are any two finite sets then n(A' ∪ B') = n((A ∩ B)') = n(U) -  n(A ∩ B)


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 Properties of Elements in Sets 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. Quadrilaterals | Four Sided Polygon | Closed Figure | Adjoining Figure

    Jul 14, 25 02:55 AM

    Square
    Quadrilaterals are known as four sided polygon.What is a quadrilateral? A closed figure made of our line segments is called a quadrilateral. For example:

    Read More

  2. Formation of Numbers | Smallest and Greatest Number| Number Formation

    Jul 14, 25 01:53 AM

    In formation of numbers we will learn the numbers having different numbers of digits. We know that: (i) Greatest number of one digit = 9,

    Read More

  3. 5th Grade Geometry Practice Test | Angle | Triangle | Circle |Free Ans

    Jul 14, 25 01:53 AM

    Name the Angles
    In 5th grade geometry practice test you will get different types of practice questions on lines, types of angle, triangles, properties of triangles, classification of triangles, construction of triang…

    Read More

  4. 5th Grade Circle Worksheet | Free Worksheet with Answer |Practice Math

    Jul 11, 25 02:14 PM

    Radii of the circRadii, Chords, Diameters, Semi-circles
    In 5th Grade Circle Worksheet you will get different types of questions on parts of a circle, relation between radius and diameter, interior of a circle, exterior of a circle and construction of circl…

    Read More

  5. Construction of a Circle | Working Rules | Step-by-step Explanation |

    Jul 09, 25 01:29 AM

    Parts of a Circle
    Construction of a Circle when the length of its Radius is given. Working Rules | Step I: Open the compass such that its pointer be put on initial point (i.e. O) of ruler / scale and the pencil-end be…

    Read More