An interactive adventure in mathematical logic for Grade 9–10 students. Learn, explore, and master Sets through games and real-life examples!
Start here! Explore the definition of sets, types of sets, and all set operations with real-life examples from sports, food, and hobbies.
Interactive animated Venn diagrams. Click regions to highlight Union, Intersection, Difference, and Complement. Drag objects into sets!
Step-by-step solutions to 20 two-set and 20 three-set word problems. See every step revealed one at a time!
Test your knowledge with Multiple Choice, Fill in the Blank, and Drag & Drop quizzes. Earn XP and unlock badges!
Roster & Set-builder form, membership, cardinality
All elements in A OR B (or both)
Elements in BOTH A and B
Elements in A but NOT in B
Everything NOT in A
Relationships between sets
A set is a well-defined collection of distinct objects. These objects are called elements or members of the set.
List all elements inside curly braces.
Real life: A = {Football, Cricket, Tennis} — sports Aarav plays
Describe elements by a rule or property.
Read as: “A is the set of all x such that x is an even number less than or equal to 10”
3 ∈ A means “3 is an element of A”
7 ∉ A means “7 is NOT in A”
Number of elements in A
A set with no elements
Contains all elements under discussion
A ⊆ B: every element of A is in B
A set with NO elements.
A = { } or A = ∅Example: Set of students who are 5 meters tall
A set with exactly ONE element.
A = {7}Example: Set of even prime numbers = {2}
A set with a countable (limited) number of elements.
A = {1, 2, 3, 4, 5}Example: Days of the week = {Mon, Tue, …, Sun}
A set with unlimited elements.
N = {1, 2, 3, 4, …}Example: Set of all natural numbers
Contains ALL elements under consideration.
U = {1,2,3,…,10}Example: All students in a school class
Two sets with EXACTLY the same elements.
A = B{1,2,3} = {3,1,2} ✓ (order doesn’t matter)
Sets with the SAME number of elements (same cardinality).
n(A) = n(B){a,b,c} ~ {1,2,3} since both have 3 elements
Joint: Have at least one common element.
Disjoint: A∩B = ∅, no common elements.
Let’s use: U = All 30 students in a class
A = {students who play Cricket} = {Aarav, Bina, Chetan, Diya, Esha}
B = {students who play Football} = {Bina, Diya, Farhan, Geeta, Harsh}
All students who play Cricket OR Football (or both)
Students who play BOTH Cricket AND Football
Students in Cricket but NOT in Football
Students who do NOT play Cricket (in U but not in A)
Set A is a subset of B (written A ⊆ B) if every element of A is also in B.
The power set P(A) is the set of ALL possible subsets of A, including ∅ and A itself.
| n(A) | Subsets | Proper Subsets |
| 0 | 1 | 0 |
| 1 | 2 | 1 |
| 2 | 4 | 3 |
| 3 | 8 | 7 |
| n | 2ⁿ | 2ⁿ−1 |
The complement of a union equals the intersection of complements, and vice versa!
A = {Football, Cricket, Tennis, Hockey, Badminton} | B = {Cricket, Hockey, Basketball, Volleyball, Table Tennis} | U = All 15 sports
A = Math lovers | B = Science lovers | C = Art lovers
Drag the items into the correct region: Only A, A∩B, or Only B. Use the topic: Sports students play.
A = Students who like Maths | B = Students who like Science | C = Students who like Art
Drag each student into their correct region!
Drag each description to the correct set operation name.
Real-time overview of student progress and activity. All data updates as students interact with the page.
Generate a printable worksheet with selected problems. Choose difficulty and topic, then print or save as PDF.