Python - Set Operators

In Python, the set operations contain the union, intersection, difference, and symmetric difference. Python implements them with following set operators −

Python Set Union Operator (|)

The union of two sets is a set containing all elements that are in A or in B or both. For example,

{1,2}∪{2,3}={1,2,3}

The following diagram illustrates the union of two sets.

Union Of Two Sets

Python uses the "|" symbol as a union operator. The following example uses the "|" operator and returns the union of two sets.

Example

s1 = {1,2,3,4,5}
s2 = {4,5,6,7,8}
s3 = s1 | s2
print ("Union of s1 and s2: ", s3)

It will produce the following output −

Union of s1 and s2: {1, 2, 3, 4, 5, 6, 7, 8}

Python Set Intersection Operator (&)

The intersection of two sets AA and BB, denoted by A∩B, consists of all elements that are both in A and B. For example,

{1,2}∩{2,3}={2}

The following diagram illustrates intersection of two sets.

Intersection Operator

Python uses the "&" symbol as an intersection operator. Following example uses & operator and returns intersection of two sets.

s1 = {1,2,3,4,5}
s2 = {4,5,6,7,8}
s3 = s1 & s2
print ("Intersection of s1 and s2: ", s3)

It will produce the following output −

Intersection of s1 and s2: {4, 5}

Python Set Difference Operator (-)

The difference (subtraction) is defined as follows. The set A−B consists of elements that are in A but not in B. For example,

If A={1,2,3} and B={3,5}, then A−B={1,2}

The following diagram illustrates difference of two sets −

difference_operator

Python uses the "-" symbol as a difference operator.

Example

The following example uses the "-" operator and returns difference of two sets.

s1 = {1,2,3,4,5}
s2 = {4,5,6,7,8}
s3 = s1 - s2
print ("Difference of s1 - s2: ", s3)
s3 = s2 - s1
print ("Difference of s2 - s1: ", s3)

It will produce the following output −

Difference of s1 - s2: {1, 2, 3}
Difference of s2 - s1: {8, 6, 7}

Note that "s1-s2" is not the same as "s2-s1".

Python Set Symmetric Difference Operator

The symmetric difference of A and B is denoted by "A Δ B" and is defined by

A Δ B = (A − B) ⋃ (B − A)

If A = {1, 2, 3, 4, 5, 6, 7, 8} and B = {1, 3, 5, 6, 7, 8, 9}, then A Δ B = {2, 4, 9}.

The following diagram illustrates the symmetric difference between two sets −

Symmetric Difference

Python uses the "^" symbol as a symbolic difference operator.

Example

The following example uses the "^" operator and returns symbolic difference of two sets.

s1 = {1,2,3,4,5}
s2 = {4,5,6,7,8}
s3 = s1 - s2
print ("Difference of s1 - s2: ", s3)
s3 = s2 - s1
print ("Difference of s2 - s1: ", s3)
s3 = s1 ^ s2
print ("Symmetric Difference in s1 and s2: ", s3)

It will produce the following output −

Difference of s1 - s2: {1, 2, 3}
Difference of s2 - s1: {8, 6, 7}
Symmetric Difference in s1 and s2: {1, 2, 3, 6, 7, 8}
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