Intersection of Sets

Definition of Intersection of Sets:

Intersection of two given sets is the largest set which contains all the elements that are common to both the sets.

To find the intersection of two given sets A and B is a set which consists of all the elements which are common to both A and B.

The symbol for denoting intersection of sets is ‘‘.

For example:

Let set A = {2, 3, 4, 5, 6}

and set B = {3, 5, 7, 9}

In this two sets, the elements 3 and 5 are common. The set containing these common elements i.e., {3, 5} is the intersection of set A and B.

The symbol used for the intersection of two sets is ‘‘.

Therefore, symbolically, we write intersection of the two sets A and B is A ∩ B which means A intersection B. 

The intersection of two sets A and B is represented as A ∩ B = {x : x ∈ A and x ∈ B} 

Solved examples to find intersection of two given sets:

1. If A = {2, 4, 6, 8, 10} and B = {1, 3, 8, 4, 6}. Find intersection of two set A and B. 

Solution:

A ∩ B = {4, 6, 8}

Therefore, 4, 6 and 8 are the common elements in both the sets. 

2. If X = {a, b, c} and Y = {ф}. Find intersection of two given sets X and Y. 

Solution:

X ∩ Y = { } 

3. If set A = {4, 6, 8, 10, 12}, set B = {3, 6, 9, 12, 15, 18} and set C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

(i) Find the intersection of sets A and B.

(ii) Find the intersection of two set B and C.

(iii) Find the intersection of the given sets A and C.

Solution:

(i) Intersection of sets A and B is A ∩ B

Set of all the elements which are common to both set A and set B is {6, 12}.

(ii) Intersection of two set B and C is B ∩ C

Set of all the elements which are common to both set B and set C is {3, 6, 9}.

(iii) Intersection of the given sets A and C is A ∩ C

Set of all the elements which are common to both set A and set C is {4, 6, 8, 10}.


Notes:

A ∩ B is a subset of A and B. 

Intersection of a set is commutative, i.e., A ∩ B = B ∩ A. 

Operations are performed when the set is expressed in the roster form.



Some properties of the operation of intersection

(i) A∩B = B∩A (Commutative law) 

(ii) (A∩B)∩C = A∩ (B∩C) (Associative law) 

(iii) ϕ ∩ A = ϕ (Law of ϕ) 

(iv) U∩A = A (Law of ∪) 

(v) A∩A = A (Idempotent law) 

(vi) A∩(B∪C) = (A∩B) ∪ (A∩C) (Distributive law) Here ∩ distributes over ∪

Also, A∪(B∩C) = (AUB) ∩ (AUC) (Distributive law) Here ∪ distributes over ∩ 

Notes:

A ∩ ϕ = ϕ ∩ A = ϕ i.e. intersection of any set with the empty set is always the empty set.

Set Theory

Sets

Objects Form a Set

Elements of a Set

Properties of Sets

Representation of a Set

Different Notations in Sets

Standard Sets of Numbers

Types of Sets

Pairs of Sets

Subset

Subsets of a Given Set

Operations on Sets

Union of Sets

Difference of two Sets

Complement of a Set

Cardinal number of a set

Cardinal Properties of Sets

Venn Diagrams



7th Grade Math Problems

From Definition of Intersection of 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. Thousandths Place in Decimals | Decimal Place Value | Decimal Numbers

    Jul 20, 24 03:45 PM

    Thousandths Place in Decimals
    When we write a decimal number with three places, we are representing the thousandths place. Each part in the given figure represents one-thousandth of the whole. It is written as 1/1000. In the decim…

    Read More

  2. Hundredths Place in Decimals | Decimal Place Value | Decimal Number

    Jul 20, 24 02:30 PM

    Hundredths Place in Decimals
    When we write a decimal number with two places, we are representing the hundredths place. Let us take plane sheet which represents one whole. Now, we divide the sheet into 100 equal parts. Each part r…

    Read More

  3. Tenths Place in Decimals | Decimal Place Value | Decimal Numbers

    Jul 20, 24 12:03 PM

    Tenth Place in Decimals
    The first place after the decimal point is tenths place which represents how many tenths are there in a number. Let us take a plane sheet which represents one whole. Now, divide the sheet into ten equ…

    Read More

  4. Representing Decimals on Number Line | Concept on Formation of Decimal

    Jul 20, 24 10:38 AM

    Representing decimals on number line shows the intervals between two integers which will help us to increase the basic concept on formation of decimal numbers.

    Read More

  5. Decimal Place Value Chart |Tenths Place |Hundredths Place |Thousandths

    Jul 20, 24 01:11 AM

    Decimal place value chart
    Decimal place value chart are discussed here: The first place after the decimal is got by dividing the number by 10; it is called the tenths place.

    Read More