Unit 11.2A · Term 2

Set Operations & Comparison

Set operations let you combine, compare, and filter collections of data. Python supports all standard mathematical set operations: union, intersection, difference, and symmetric difference.

Learning Objectives

11.2.1.3 Use operations on sets
11.2.1.4 Compare sets

Lesson Presentation

11.2A-lesson-10-set-operations.pdf · Slides for classroom use

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Conceptual Anchor

The Venn Diagram

Every set operation corresponds to a region in a Venn diagram. Union = everything in both circles. Intersection = the overlapping middle. Difference = one circle minus the overlap. Symmetric difference = both circles minus the overlap.

Rules & Theory

Set Operations

Operation	Method	Operator	Result
Union	`A.union(B)`	`A \| B`	All elements from both sets
Intersection	`A.intersection(B)`	`A & B`	Elements common to both
Difference	`A.difference(B)`	`A - B`	Elements in A but not in B
Symmetric Difference	`A.symmetric_difference(B)`	`A ^ B`	Elements in A or B but not both

A = {1, 2, 3, 4, 5}
B = {4, 5, 6, 7, 8}

print(A | B)     # {1, 2, 3, 4, 5, 6, 7, 8}  — Union
print(A & B)     # {4, 5}                      — Intersection
print(A - B)     # {1, 2, 3}                   — Difference (A not B)
print(B - A)     # {6, 7, 8}                   — Difference (B not A)
print(A ^ B)     # {1, 2, 3, 6, 7, 8}          — Symmetric difference

Set Comparison

Operation	Method	Operator	True when…
Subset	`A.issubset(B)`	`A <= B`	All elements of A are in B
Proper subset	—	`A < B`	A ⊂ B and A ≠ B
Superset	`A.issuperset(B)`	`A >= B`	All elements of B are in A
Disjoint	`A.isdisjoint(B)`	—	No common elements
Equality	—	`A == B`	Same elements (order irrelevant)

A = {1, 2, 3}
B = {1, 2, 3, 4, 5}
C = {6, 7}

print(A <= B)          # True — A is a subset of B
print(A < B)           # True — A is a proper subset (A ≠ B)
print(B >= A)          # True — B is a superset of A
print(A.isdisjoint(C)) # True — no common elements
print({3, 2, 1} == A)  # True — same elements, order doesn't matter

Update Operations

Add _update to modify the set in-place: A.update(B) is like A = A | B. Similarly: intersection_update(), difference_update(), symmetric_difference_update().

Worked Examples

1 Finding Common Students

math_class = {"Ali", "Dana", "Marat", "Aisha", "Bolat"}
cs_class = {"Aisha", "Bolat", "Kamila", "Dias", "Ali"}

# Who takes BOTH classes?
both = math_class & cs_class
print("Both:", both)       # {'Ali', 'Aisha', 'Bolat'}

# Who takes EITHER class?
any_class = math_class | cs_class
print("Any:", any_class)   # All 7 unique names

# Who takes Math but NOT CS?
math_only = math_class - cs_class
print("Math only:", math_only)  # {'Dana', 'Marat'}

2 Checking Subsets

required = {"Math", "Science", "English"}
student_courses = {"Math", "Science", "English", "Art", "PE"}

if required <= student_courses:
    print("All required courses are taken ✓")
else:
    missing = required - student_courses
    print("Missing courses:", missing)

3 Unique Characters in Two Strings

s1 = set(input("Word 1: ").lower())  # e.g., "hello"
s2 = set(input("Word 2: ").lower())  # e.g., "world"

print("Common letters:", s1 & s2)         # {'l', 'o'}
print("Only in word 1:", s1 - s2)         # {'h', 'e'}
print("In either (not both):", s1 ^ s2)   # {'h', 'e', 'w', 'r', 'd'}

Pitfalls & Common Errors

Difference is NOT Symmetric

A - B ≠ B - A. A - B gives elements in A but not B. B - A gives elements in B but not A. These are usually different!

Confusing | and &

| (union) gives all elements. & (intersection) gives only common elements. Think: | = OR (inclusive), & = AND (restrictive).

Pro-Tips for Exams

Set Operation Strategy

Draw a Venn diagram for complex set problems
A | B always has len(A | B) ≤ len(A) + len(B)
A & B always has len(A & B) ≤ min(len(A), len(B))
A ^ B = (A | B) - (A & B) — everything except the overlap
Subset check A <= B is the fastest way to test "all of A is in B"

Graded Tasks

Remember

Name the 4 set operations and their Python operators.

Understand

Given A = {1,2,3,4} and B = {3,4,5,6}, calculate by hand: A|B, A&B, A-B, A^B.

Apply

Write a program that reads two lists of friends and outputs: (a) mutual friends, (b) friends unique to each person.

Analyze

Is it true that (A - B) | (B - A) == A ^ B for any sets A, B? Prove with an example.

Create

Build a "skill matcher" program: input required skills for a job and a candidate's skills. Output matched, missing, and extra skills using set operations.

Self-Check Quiz

1. What does {1,2,3} | {3,4,5} give?

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2. What does {1,2,3} & {3,4,5} give?

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3. Is {1,2} <= {1,2,3} True or False?

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4. What does {1,2,3} - {2,3,4} give?

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5. What does isdisjoint() check?

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