# Intersection of Sets

Intersection of Sets : The set consisting of all elements which are in both sets A and B. It is denoted by A ∩ B
( read as A intersection B ).

If set A and B are subsets of the universal set U and A and B are disjoint sets then A ∩ B = Φ

Properties of intersection of sets

1) A ∩ A = A

2) A ∩ Φ = Φ

3) A ∩ B = B ∩ A ( Commutative property for intersection)

4) ( A ∩ B) ∩C = A ∩ ( B ∩C ) ( Associative property )

5) A ∩ ( B ∪ C ) = ( A ∩ B ) ∪ ( A ∩ C ) (Distributive law )
i.e ∩ distributes over ∪

Examples :

1) If A = { 1, 2, 3, 4 } and B = { x | x is an even natural number} then
find A ∩ B.

Solution :
A = { 1, 2, 3, 4 }

B = { x | x is an even natural number}

B = { 2, 4, 6, 8, … }

The common elements between set A and B are 2 and 4.

∴ A ∩ B = { 2, 4}

2) If P = { x | x is a multiple of 10 } and
Q = { x | the unit’s (ones place )digit of x is not zero} then find A ∩ B.

Solution :
P = { x | x is a multiple of 10 }

P = { 10, 20, 30, 40, 50, … }

Q = { x | the unit’s (ones place )digit of x is not zero}

Q = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12,… } ---> all elements except 10,20,30,…

So, there is no common element between set A and B.

∴ P ∩ Q = Φ

Set Theory

Sets
Representation of Set
Cardinal Number
Types of Sets
Pairs of Sets
Subset
Complement of Set
Union of the Sets
Intersection of Sets
Operations on Sets
De Morgan's Law
Venn Diagrams
Venn-diagrams for sets
Venn-diagrams for different situations
Problems on Intersection of Two Sets