Set Algebra — union(), intersection(), difference(), and more

What you will learn

Union · Intersection · Difference · Symmetric Difference · Subsets

Set algebra is one of Python's most useful features for comparing groups of data. Think of it as mathematics with collections.

Symbol	Meaning
`	`
&	Intersection — shared only
-	Difference — left exclusive
^	Symmetric difference — one side only

Memory formula: | = ALL · & = BOTH · - = ONLY ME · ^ = EITHER ONE

After File 09 — Set Methods, you can add and remove set members. This lesson compares whole groups with algebra.

Learning roadmap

1. The Venn diagram you must remember

We'll use these two sets throughout the lesson:

cricket = {"A", "B", "C", "D"}
tennis  = {"C", "D", "E", "F"}

2. Union (|) — everyone together

Union means combine everything without duplicates.

cricket = {"A", "B", "C", "D"}
tennis  = {"C", "D", "E", "F"}

print(cricket | tennis)
print(cricket.union(tennis))

Output:

{'A', 'B', 'C', 'D', 'E', 'F'}

Both expressions produce the same result.

Operator	Method
`a	b`

3. Intersection (&) — common elements

Intersection means only the shared values.

print(cricket & tennis)           # {'C', 'D'}
print(cricket.intersection(tennis))

Think of interview attendance:

• Cricket players = invited
• Tennis players = registered
• Intersection = invited and registered

4. Difference (-) — only me

Difference removes everything that exists in the second set.

Cricket only

print(cricket - tennis)  # {'A', 'B'}

Tennis only

print(tennis - cricket)  # {'E', 'F'}

Order matters!

Expression	Result
A - B	Only A's exclusive elements
B - A	Only B's exclusive elements

5. Symmetric difference (^) — exactly one group

This is the most confusing operator for beginners.

Present in A OR B, but NOT BOTH.

print(cricket ^ tennis)  # {'A', 'B', 'E', 'F'}

Think of students choosing clubs:

• Both clubs → removed
• Only one club → kept

6. All four operations together

Symbol	Name	Meaning
`	`	Union
&	Intersection	Shared
-	Difference	Only left
^	Symmetric difference	Exclusive

7. Subset and superset

These do not create new sets — they return True or False.

A = {10, 20, 30}
B = {10, 20}

print(B.issubset(A))    # True
print(A.issuperset(B))  # True
print(B <= A)           # True — operator form
print(A >= B)           # True

Relationship	Meaning
Subset	Small inside big
Superset	Big contains small

8. Disjoint sets

Disjoint means no common values.

a = {1, 2}
b = {7, 8}

print(a.isdisjoint(b))  # True

If there is even one common value:

a = {1, 2, 3}
b = {3, 8}

print(a.isdisjoint(b))  # False

9. Methods vs operators

Both styles are equally valid.

Operator	Method
`a	b`
a & b	a.intersection(b)
a - b	a.difference(b)
a ^ b	a.symmetric_difference(b)

In-place update variants

Operator	In-place method
`a	= b`
a &= b	a.intersection_update(b)
a -= b	a.difference_update(b)
a ^= b	a.symmetric_difference_update(b)

Which should you use?

• Short code: operators (|, &, -, ^)
• Readable beginner code: methods (union(), intersection())

Mini project — sports club analytics

Imagine a school database.

cricket = {"Ravi", "Anil", "Sunil", "Sachin"}
football = {"Sachin", "Rahul", "Vijay", "Sunil"}

print("All students:", cricket | football)
print("Dual players:", cricket & football)
print("Only cricket:", cricket - football)
print("Only football:", football - cricket)
print("Exactly one sport:", cricket ^ football)

Expected results

Question	Expression
Total unique players	`cricket
Play both sports	cricket & football
Cricket only	cricket - football
Football only	football - cricket
One sport only	cricket ^ football

One-page revision sheet

Remember these four symbols:

a | b

a & b

a - b

a ^ b

Task	Syntax
All unique	`a
Shared only	a & b
Left exclusive	a - b
One side only	a ^ b
Subset check	b.issubset(a)
No overlap	a.isdisjoint(b)

Common interview mistakes

Mistake 1 — confusing - with ^:

a - b   # only left-side exclusive elements
a ^ b   # both exclusive sides — removes overlap

Mistake 2 — thinking union() changes the original set:

a.union(b)   # returns NEW set
a.update(b)  # mutates a in place
a |= b       # same as update

Practice questions

Test yourself before File 11 — Frozenset Methods:

1. Which operator returns all unique elements?
2. What is the difference between A - B and B - A?
3. Which operation removes the common values and keeps only exclusive ones?
4. What does issubset() return?
5. Which method checks whether two sets have no overlap?

Knowledge check

Q1: Operator for all unique elements?
Answer: | (union).

Q2: A - B vs B - A?
Answer: Direction matters — each returns only the left set's exclusive elements.

Q3: Remove common values, keep exclusive?
Answer: ^ (symmetric difference).

Q4: issubset() return type?
Answer: True or False.

Q5: Check no overlap?
Answer: isdisjoint().