Python Set Intersection()

February 2, 2021

Intersection() of a Set

The intersection() of two or more sets returns a set that contains all common items from all the sets.

The result set contains a distinct element that is, the item that is present in all sets, the result will contain only one appearance of this item.

∩ the symbol denotes the intersection of sets.

Let us understand this concept with an example, suppose there are two sets A and B, we have to find A ∩ B.

A = { 1 , 2, 3, 4, 5 }

B = { 1, 3, 5, 7, 9 }

A ∩ B = { 1, 3, 5 }

Syntax :

set1.intersection(set2,set3,…)

The parameter can be only one or more. You can compare as many sets as you like. Separate each set with a comma.

Return Type :

The intersection() method returns a new set with all the common elements from the set and all other sets (passed as an argument).

If the argument is not passed to the intersection(), it returns a shallow copy of the set.

Using the & operator

#intersection of sets using & operator

#example 1
set1 = {‘P’, ‘Y’, ‘T’, ‘H’, ‘O’, ‘N’ }
set2 = {‘C’, ‘O’, ‘D’, ‘I’, ‘N’, ‘G’ }
print( set1 & set2 )

#example 2
A = { 2, 4, 6, 8, 10, 11, 12 }
B = { 3, 6, 9, 12, 15 }
C = { 4, 8, 12, 16 }
print( A & B & C )

Output :

{'N', 'O'}

{12}

Using intersection() function

#intersection of sets using intersection() method

#example 1
set1 = {‘P’, ‘Y’, ‘T’, ‘H’, ‘O’, ‘N’ }
set2 = {‘C’, ‘O’, ‘D’, ‘I’, ‘N’, ‘G’ }
print( set1.intersection(set2) )

#example 2
A = { 2, 4, 6, 8 , 10, 12, 14, 16, 18, 20 }
B = { 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 }
C = { 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 }
print( A.intersection(B,C) )

Output :

{'N', 'O'}

{12}

Intersection of three sets

A , B, C are three sets having some elements.

Approach:

First Calculate intersection of two sets (A ∩ B) and store it in any set say X.
Then find intersection of X and the third set i.e. (X ∩ C).

A ∩ B ∩ C = (A ∩ B) ∩ C = A ∩ (B ∩ C) = (A ∩ C) ∩ B

#intersection of three sets
A = { 2, 4, 6, 8 , 10, 12, 14, 16, 18, 20 }
B = { 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 }
C = { 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 }

#A & B
x=A.intersection(B)
print(“A intersectionb B : “,x)

#A & C
y=A.intersection(C)
print(“A intersectionb C : “,y)

#B & C
z=B.intersection(C)
print(“B intersectionb C : “,z)

#( A & B ) & C = A & B & C
print(“( A & B ) & C  : “,x.intersection(C))

#( A & C ) & B = A & B & C
print(“( A & C ) & B  : “,y.intersection(B))

# A & ( B  & C ) = A & B & C
print(“A & ( B  & C ) : “,z.intersection(A))

#A & B & C
print( “A & B & C     : “,A.intersection(B,C) )

Output :

A intersectionb B :  {18, 12, 6}
A intersectionb C :  {4, 8, 12, 16, 20}
B intersectionb C :  {24, 12}

(A & B) & C :  {12}
(A & C) & B :  {12}
A & (B & C) :  {12}
A & B & C   :  {12}