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
● Subset
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.
Mar 02, 24 05:31 PM
Mar 02, 24 04:36 PM
Mar 02, 24 03:32 PM
Mar 01, 24 01:42 PM
Feb 29, 24 05:12 PM
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.