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

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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