Question

Properties of intersection of sets with eaxample

Answer 1

Intersection of Sets
The intersection of two sets A and B ( denoted by A∩B ) is the set of all elements that is common to both A and B. In mathematical form,

For two sets A and B,
A∩B = { x: x∈A and x∈B }
Shaded part demonstrates the intersection between two sets

Similarly for three sets A, B and C,

A∩B∩C = { x: x∈A and x∈B and x∈C }
Venn diagram showing intersection of three sets where shaded part denotes the intersection

Intersection of Sets Examples
Example #1: Intersection of Two Sets With Venn Diagram
If A = {a, b, c, d, e} and B = {d, e, f, g}, find A∩B.

Here,
A = {a, b, c, d, e}
B = {d, e, f, g}
Now,
A∩B = {a, b, c, d, e} ∩ {d, e, f, g}
∴ A∩B = {d, e}
Example showing of intersection of two sets where shaded part shows the intersection.

Example #2
Suppose A = { x: x is an integer between 1 and 7} and B = { x: x is an integer between 4 and 9} then, find A∩B.

Here,
A = {2, 3, 4, 5, 6}
B = {5, 6, 7, 8}
∴ A∩B = {5, 6} = { x: x is an integer between 4 and 7}