Python Basics — Set Operations

3 minute read

Set Operations

Python sets support mathematical set operations: union, intersection, difference, and symmetric difference.

Union (|)

All elements from both sets:

a = {1, 2, 3}
b = {3, 4, 5}

print(a | b)            # {1, 2, 3, 4, 5}
print(a.union(b))       # {1, 2, 3, 4, 5}

Intersection (&)

Elements common to both sets:

a = {1, 2, 3, 4}
b = {3, 4, 5, 6}

print(a & b)                # {3, 4}
print(a.intersection(b))    # {3, 4}

Difference (-)

Elements in the first set but not in the second:

a = {1, 2, 3, 4}
b = {3, 4, 5, 6}

print(a - b)              # {1, 2}
print(a.difference(b))    # {1, 2}

print(b - a)              # {5, 6}  (order matters!)

Symmetric Difference (^)

Elements in either set, but not in both:

a = {1, 2, 3, 4}
b = {3, 4, 5, 6}

print(a ^ b)                        # {1, 2, 5, 6}
print(a.symmetric_difference(b))    # {1, 2, 5, 6}

Visual Summary

a = {1, 2, 3, 4}
b = {3, 4, 5, 6}

Union (a | b):         {1, 2, 3, 4, 5, 6}   — everything
Intersection (a & b):  {3, 4}                — overlap
Difference (a - b):    {1, 2}                — only in a
Sym Diff (a ^ b):      {1, 2, 5, 6}          — not shared

Operator vs Method Syntax

Operation Operator Method
Union a \| b a.union(b)
Intersection a & b a.intersection(b)
Difference a - b a.difference(b)
Symmetric Diff a ^ b a.symmetric_difference(b)

The method syntax accepts any iterable, while operators require sets:

a = {1, 2, 3}

# Method accepts iterable
print(a.union([3, 4, 5]))  # {1, 2, 3, 4, 5}

# Operator requires set
# print(a | [3, 4, 5])  # TypeError
print(a | set([3, 4, 5]))  # {1, 2, 3, 4, 5}

Subset and Superset

a = {1, 2}
b = {1, 2, 3, 4}

# Subset: all elements of a are in b
print(a <= b)          # True
print(a.issubset(b))   # True

# Proper subset (subset and not equal)
print(a < b)           # True

# Superset: b contains all elements of a
print(b >= a)          # True
print(b.issuperset(a)) # True

# Proper superset
print(b > a)           # True

# Equal sets
print({1, 2} <= {1, 2})  # True (subset)
print({1, 2} < {1, 2})   # False (not proper subset)

Disjoint Sets

Two sets with no common elements:

a = {1, 2, 3}
b = {4, 5, 6}
c = {3, 4, 5}

print(a.isdisjoint(b))  # True (no overlap)
print(a.isdisjoint(c))  # False (3 is common)

Real-World Use Cases

Finding Common Interests

alice_hobbies = {"reading", "hiking", "cooking", "chess"}
bob_hobbies = {"gaming", "hiking", "cooking", "cycling"}

common = alice_hobbies & bob_hobbies
print(f"Common hobbies: {common}")
# Common hobbies: {'hiking', 'cooking'}

only_alice = alice_hobbies - bob_hobbies
print(f"Alice's unique: {only_alice}")
# Alice's unique: {'reading', 'chess'}

Deduplication Check

emails = ["a@x.com", "b@x.com", "a@x.com", "c@x.com"]
unique = set(emails)
duplicates = len(emails) - len(unique)
print(f"Found {duplicates} duplicate(s)")  # Found 1 duplicate(s)

Permission Checking

required = {"read", "write"}
user_perms = {"read", "write", "execute"}

if required <= user_perms:
    print("Access granted")  # Access granted
else:
    missing = required - user_perms
    print(f"Missing permissions: {missing}")

Multiple Set Operations

a = {1, 2, 3}
b = {2, 3, 4}
c = {3, 4, 5}

# Union of multiple sets
print(a | b | c)  # {1, 2, 3, 4, 5}
print(a.union(b, c))  # {1, 2, 3, 4, 5}

# Intersection of multiple sets
print(a & b & c)  # {3}
print(a.intersection(b, c))  # {3}

Summary

  • Union (|): all elements from both sets
  • Intersection (&): elements common to both
  • Difference (-): elements in first but not second
  • Symmetric difference (^): elements in either but not both
  • Subset (<=), superset (>=), disjoint (.isdisjoint())
  • Methods accept any iterable; operators require sets

Next up: Set Methods →

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