PY-L2-09 · Set Operations — Union, Intersection, Difference

Set Operations — Union, Intersection, Difference

Yesterday a set was a list with no duplicates. Today we combine and compare them. The Venn-diagram operators you saw in maths class — |, &, -, ^— work directly on Python sets. Each one is a one-character answer to a question like "who's in both?" or "who's in mine but not yours?"

⏱ 1 hour🟢🔵 Concept lesson📚 After PY-L2-08💻 VS Code or online-python.com

Learning Goals

3 min

By the end of this lesson you can:

Combine sets with union (|) — "everyone in either".
Overlap sets with intersection (&) — "everyone in both".
Subtract sets with difference (-) — "in mine, not yours".
Find the "exactly one" group with symmetric difference (^) — "in one but not both".

Warm-Up

5 min

Two clubs at school. Some kids are in both, some in only one.

chess = {"Aisyah", "Wei Jie", "Priya", "Iman"}
robot = {"Wei Jie", "Iman", "Aizat", "Hafiz"}

Predict the output — read each operator out loud:

print(chess | robot)   # everyone in either club
print(chess & robot)   # in BOTH clubs
print(chess - robot)   # chess kids who aren't in robot
print(chess ^ robot)   # in exactly ONE of the two

Show the answer

{'Aisyah', 'Hafiz', 'Wei Jie', 'Priya', 'Aizat', 'Iman'}
{'Wei Jie', 'Iman'}
{'Aisyah', 'Priya'}
{'Aisyah', 'Hafiz', 'Priya', 'Aizat'}

Four set operators, four answers — none of them needed a loop. The order of names inside each set may vary on your machine; sets don't track order.

Today's big idea

Set operations are collection algebra. Each one replaces a small loop that you'd otherwise have to write by hand.

New Concept · Four Operators

14 min

1 · Union — `a | b`

Every item in a, every item in b, with no duplicates. Read it as "a or b".

fruits   = {"apple", "banana", "cherry"}
imported = {"banana", "kiwi", "mango"}

stocked = fruits | imported
print(stocked)
# → {'apple', 'banana', 'cherry', 'kiwi', 'mango'}

The same operator has a wordy twin: fruits.union(imported). Use whichever your eyes prefer.

2 · Intersection — `a & b`

Only the items that appear in both sets. Read it as "a and b".

maths   = {"Aisyah", "Priya", "Iman", "Wei Jie"}
science = {"Iman", "Priya", "Hafiz", "Aizat"}

both = maths & science
print(both)
# → {'Iman', 'Priya'}

Wordy form: maths.intersection(science).

3 · Difference — `a - b`

The items that are in a but not in b. Read it as "in a, not in b". Order matters here — b - a is usually a different answer.

bought = {"egg", "milk", "rice", "salt"}
have   = {"milk", "salt", "soy sauce"}

still_to_buy = bought - have
print(still_to_buy)
# → {'egg', 'rice'}

Wordy form: bought.difference(have).

4 · Symmetric difference — `a ^ b`

Items in exactly one of the sets — never both. Read it as "in a or b, but not both".

monday = {"Aisyah", "Wei Jie", "Priya"}
friday = {"Wei Jie", "Iman", "Priya"}

attended_only_one = monday ^ friday
print(attended_only_one)
# → {'Aisyah', 'Iman'}

Wordy form: monday.symmetric_difference(friday).

The cheat-sheet

Question                        Operator   Words
"Combine both"                  a | b      union
"What's in both?"               a & b      intersection
"In mine, not theirs"           a - b      difference
"In exactly one"                a ^ b      symmetric difference
"Is a a subset of b?"           a <= b     issubset
"Is a a superset of b?"         a >= b     issuperset

Subset and superset

Two extras worth knowing. a <= b asks "is every element of a also in b?" — i.e. is a a subset of b? a >= b reverses the question. Both return True or False.

small = {"a", "b"}
big   = {"a", "b", "c", "d"}
print(small <= big)    # → True   (every letter in small is in big)
print(big   >= small)  # → True   (big contains all of small)
print(small >= big)    # → False

Read like Venn diagrams

Every set operator has a clean Venn-diagram picture: union is both circles together, intersection is the lens in the middle, difference is one whole circle minus the lens, symmetric difference is both circles minus the lens. Sketch them on paper if the operators feel new — it's genuinely the fastest way to remember which is which.

Worked Example · The Class Trip Roster

12 min

The story

Your school is running two trips this term — Zoo Negara and the Science Museum. Some pupils signed up for both, some for one, some for neither.

Cikgu Hadi wants four answers:

All the pupils going on at least one trip (union).
Both-trip-goers (intersection).
Zoo-only (difference).
One-trip-only (symmetric difference).

Save as trips.py:

Code

# trips.py — set algebra in plain English

zoo = {"Aisyah", "Wei Jie", "Priya", "Iman", "Hafiz", "Aizat"}
sci = {"Wei Jie", "Iman", "Aliya", "Daniel", "Aizat"}

print("Either trip   :", zoo | sci)
print("Both trips    :", zoo & sci)
print("Zoo only      :", zoo - sci)
print("Sci only      :", sci - zoo)
print("Exactly one   :", zoo ^ sci)
print("Did all sci-goers also pick zoo?",
      sci <= zoo)

Output (order may vary)

Either trip   : {'Hafiz', 'Daniel', 'Iman', 'Aizat', 'Aliya', 'Aisyah', 'Wei Jie', 'Priya'}
Both trips    : {'Wei Jie', 'Iman', 'Aizat'}
Zoo only      : {'Hafiz', 'Aisyah', 'Priya'}
Sci only      : {'Aliya', 'Daniel'}
Exactly one   : {'Hafiz', 'Aliya', 'Daniel', 'Aisyah', 'Priya'}
Did all sci-goers also pick zoo? False

Read the diff

Six different questions, six one-line answers. Each line is the right operator for its question — no loops, no ifs. Imagine writing this with nested loops over lists; it would be twenty lines and a head-scratch.

Update operators

Just like += and -= on numbers, sets have |=, &=, -= and ^= for "update this set in place":

zoo |= {"Maya"}      # add Maya to zoo
zoo -= {"Aisyah"}    # remove Aisyah from zoo
print(zoo)

Try It Yourself

13 min

Three exercises. Match each English sentence to a set operator.

01 🟢 Common letters

Build two sets from the words "python" and "rhythm". Print the letters they have in common.

Hint

a = set("python")
b = set("rhythm")
print(a & b)
# → {'h', 'y', 't'}

02 🟡 The shopping gap

You need {"egg", "milk", "rice", "sugar", "tea"} but the pantry already has {"milk", "salt", "tea"}. Print what's still to buy.

Hint

need = {"egg", "milk", "rice", "sugar", "tea"}
have = {"milk", "salt", "tea"}
print("Still to buy:", need - have)
# → {'egg', 'rice', 'sugar'}

Note: salt is in the pantry but not on the shopping list — set difference ignores it; that's exactly what you want.

03 🔴 Loyal customers (stretch)

Two days' sales:

monday  = {"Aisyah", "Wei Jie", "Iman", "Priya"}
tuesday = {"Wei Jie", "Aizat", "Priya", "Hafiz"}

Print: (a) loyal customers — who came both days. (b) one-day customers — who came on exactly one day. (c) total unique customers across the two days.

Hint

monday  = {"Aisyah", "Wei Jie", "Iman", "Priya"}
tuesday = {"Wei Jie", "Aizat", "Priya", "Hafiz"}

print("Loyal       :", monday & tuesday)
print("One-day only:", monday ^ tuesday)
print("Total unique:", len(monday | tuesday))

Three lines, three different operators. The exact answers your set may print can vary in order — sets don't care.

Mini-Challenge · Test-Answer Marker

8 min

Build marker.py. You've got the correct answers to a multiple-pick quiz (a set of letters) and a student's answers. Score the student.

Question: "Which of these are mammals? a) dolphin b) shark c) bat d) penguin e) whale"

correct = {"a", "c", "e"}
student = {"a", "b", "e"}

Your file must:

Print the letters the student got right — intersection.
Print the letters they missed (in the correct set but not chosen) — difference correct - student.
Print the letters they wrongly chose (chosen but not correct) — student - correct.
Calculate a score: len(right) - len(wrong), never below 0. Print it.
Print PERFECT if the student answered exactly correctly — use == between the two sets, or (student ^ correct) == set().

Stretch goal. Wrap the whole logic in a function mark(correct, student) that returns a tuple (right_set, missed_set, wrong_set, score). Test it on a perfect set.

Show one possible solution

# marker.py — score a multiple-pick answer with set algebra

correct = {"a", "c", "e"}
student = {"a", "b", "e"}

right  = correct & student
missed = correct - student
wrong  = student - correct

print("Right :", right)
print("Missed:", missed)
print("Wrong :", wrong)

score = len(right) - len(wrong)
if score < 0:
    score = 0
print("Score :", score)

if student == correct:
    print("PERFECT")

# Stretch — wrap it up
def mark(correct, student):
    r = correct & student
    m = correct - student
    w = student - correct
    s = max(0, len(r) - len(w))
    return r, m, w, s

print()
print(mark({"a", "c", "e"}, {"a", "c", "e"}))
# → ({'a', 'c', 'e'}, set(), set(), 3)

Non-negotiables: one &, two - calls, the == equality check for "perfect", and a score that uses len(). max(0, ...) is a handy way to clamp a negative score.

Recap

3 min

Four operators, four English sentences. | "in either" — union. & "in both" — intersection. - "in mine, not theirs" — difference. ^ "in exactly one" — symmetric difference. Each replaces a small loop with a single symbol. Combine them and you can answer almost any "who's in which group?" question in one line.

Vocabulary Card

union (|): The combined set — every item from either side, no duplicates.
intersection (&): The overlap — items in both sets.
difference (-): In the first set but not the second. Order matters.
symmetric difference (^): In exactly one of the sets — never both.
subset (<=) / superset (>=): "Is every item of this also in that?" (subset) and the reverse (superset).

Homework

4 min

Save a new file compare_two_classes.py. Two Form-1 classes voted for their favourite sport.

one_alpha = {"football", "badminton", "futsal", "chess",
             "esports", "hockey"}
one_beta  = {"chess", "tennis", "esports", "swimming",
             "badminton", "futsal"}

Your file must:

Print the total number of different sports mentioned across both classes (union, then len()).
Print the sports that both classes named (intersection).
Print the sports only 1-Alpha picked (difference).
Print the sports only 1-Beta picked (difference, the other way).
Print the sports voted for by exactly one class (symmetric difference).
Use <= to ask "is the set {"chess", "esports"} a subset of the things 1-Alpha voted for?" Print the boolean answer.

Stretch. Add a third class one_gamma and print the sports voted for by all three classes — chain intersections, like one_alpha & one_beta & one_gamma.

Sample · compare_two_classes.py

# compare_two_classes.py — set algebra on class votes

one_alpha = {"football", "badminton", "futsal", "chess",
             "esports", "hockey"}
one_beta  = {"chess", "tennis", "esports", "swimming",
             "badminton", "futsal"}

print("Distinct sports :", len(one_alpha | one_beta))
print("Both classes    :", one_alpha & one_beta)
print("Alpha only      :", one_alpha - one_beta)
print("Beta only       :", one_beta  - one_alpha)
print("Exactly one     :", one_alpha ^ one_beta)
print("Subset check    :", {"chess", "esports"} <= one_alpha)

# Stretch — all three classes
one_gamma = {"chess", "futsal", "esports", "skating", "badminton"}
print("All three picked:", one_alpha & one_beta & one_gamma)

Non-negotiables: one |, one &, two - (in opposite directions), one ^ and one <= check. That's all four operators plus subset, all on one page.

Set Operations — Union, Intersection, Difference

⏱ 1 hour🟢🔵 Concept lesson📚 After PY-L2-08💻 VS Code or online-python.com

Question Operator Words "Combine both" a | b union "What's in both?" a & b intersection "In mine, not theirs" a - b difference "In exactly one" a ^ b symmetric difference "Is a a subset of b?" a <= b issubset "Is a a superset of b?" a >= b issuperset

small = {"a", "b"} big = {"a", "b", "c", "d"} print(small <= big) # → True (every letter in small is in big) print(big >= small) # → True (big contains all of small) print(small >= big) # → False

# trips.py — set algebra in plain English zoo = {"Aisyah", "Wei Jie", "Priya", "Iman", "Hafiz", "Aizat"} sci = {"Wei Jie", "Iman", "Aliya", "Daniel", "Aizat"} print("Either trip :", zoo | sci) print("Both trips :", zoo & sci) print("Zoo only :", zoo - sci) print("Sci only :", sci - zoo) print("Exactly one :", zoo ^ sci) print("Did all sci-goers also pick zoo?", sci <= zoo)

Either trip : {'Hafiz', 'Daniel', 'Iman', 'Aizat', 'Aliya', 'Aisyah', 'Wei Jie', 'Priya'} Both trips : {'Wei Jie', 'Iman', 'Aizat'} Zoo only : {'Hafiz', 'Aisyah', 'Priya'} Sci only : {'Aliya', 'Daniel'} Exactly one : {'Hafiz', 'Aliya', 'Daniel', 'Aisyah', 'Priya'} Did all sci-goers also pick zoo? False

monday = {"Aisyah", "Wei Jie", "Iman", "Priya"} tuesday = {"Wei Jie", "Aizat", "Priya", "Hafiz"} print("Loyal :", monday & tuesday) print("One-day only:", monday ^ tuesday) print("Total unique:", len(monday | tuesday))

# marker.py — score a multiple-pick answer with set algebra correct = {"a", "c", "e"} student = {"a", "b", "e"} right = correct & student missed = correct - student wrong = student - correct print("Right :", right) print("Missed:", missed) print("Wrong :", wrong) score = len(right) - len(wrong) if score < 0: score = 0 print("Score :", score) if student == correct: print("PERFECT") # Stretch — wrap it up def mark(correct, student): r = correct & student m = correct - student w = student - correct s = max(0, len(r) - len(w)) return r, m, w, s print() print(mark({"a", "c", "e"}, {"a", "c", "e"})) # → ({'a', 'c', 'e'}, set(), set(), 3)

Learning Goals

Warm-Up

New Concept · Four Operators

1 · Union — a | b

2 · Intersection — a & b

3 · Difference — a - b

4 · Symmetric difference — a ^ b

The cheat-sheet

Subset and superset

Worked Example · The Class Trip Roster

The story

Read the diff

Try It Yourself

Mini-Challenge · Test-Answer Marker

Recap

Vocabulary Card

Homework

Sample · compare_two_classes.py

Learning Goals

Warm-Up

New Concept · Four Operators

1 · Union — a | b

2 · Intersection — a & b

3 · Difference — a - b

4 · Symmetric difference — a ^ b

The cheat-sheet

Subset and superset

Worked Example · The Class Trip Roster

The story

Read the diff

Try It Yourself

Mini-Challenge · Test-Answer Marker

Recap

Vocabulary Card

Homework

Sample · compare_two_classes.py

1 · Union — `a | b`

2 · Intersection — `a & b`

3 · Difference — `a - b`

4 · Symmetric difference — `a ^ b`

1 · Union — `a | b`

2 · Intersection — `a & b`

3 · Difference — `a - b`

4 · Symmetric difference — `a ^ b`