Intersection of Sets
If two sets A and B are given, then the intersection of A and B is the subset of universal set U, which consist of elements common to both A and B. It is denoted by the symbol ‘∩’. This operation is represented by:
A∩B = {x : x ∈ A and x ∈ B}
Where x is the common element of both sets A and B.
The intersection of sets A and B, can also be interpreted as:
A∩B = n(A) + n(B) – n(A∪B)
Where,
n(A) = cardinal number of set A,
n(B) = cardinal number of set B,
n(A∪B) = cardinal number of union of set A and B.
Example: Let A = {1,2,3} and B = {3,4,5}
Solution:
A ∩ B = {1,2,3} ∩ {3,4,5}
A ∩ B = {3}
Then, A ∩ B = {3}; because 3 is common to both the sets.
Venn Diagram of Intersection of sets
Examples
1. If A = {a, b, d, e, g, h} B = {b, c, e, f, h, i, j}. Find A ∩ B using the Venn Diagram?
Solution:
Given Sets are A = {a, b, d, e, g, h} B = {b, c, e, f, h, i, j}
Draw the Venn Diagram for the given Sets and then find the Intersection of Sets.
Intersection is nothing but the elements that are common in both Sets A and B.
A ∩ B = { b, e, h}
2. If C = { 3, 5, 7} D = { 7, 9, 11}. Find C ∩ D using Venn Diagram?
Solution:
Given Sets are C = { 3, 5, 7} D = { 7, 9, 11}
Let us represent the given sets in the diagrammatic representation of sets
Intersection is nothing but the elements that are common in both Sets C and D.
C ∩ D = {7}