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Set Theory Fundamentals
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Set Theory Fundamentals
📚 Part 1: Set Notation and Basic Concepts
1. Which of the following correctly describes a set?
A collection of well-defined objects
A list of random numbers
Any group of items
A mathematical equation
2. Given A = {2, 4, 6, 8} and B = {4, 2, 8, 6}, what can you say about sets A and B?
They are equal sets
They are equivalent sets only
They are neither equal nor equivalent
A is a subset of B only
3. If the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {2, 4, 6, 8, 10}, find A'.
A' = { _________________ }
4. Match the correct set symbol to its meaning:
∈
⊆
∪
∩
Union
Intersection
Is an element of
Is a subset of
✏️ Part 2: Set Operations
5. Given P = {a, b, c, d} and Q = {c, d, e, f}, find:
a) P ∪ Q = { _________________ }
b) P ∩ Q = { _________________ }
6. List all possible subsets of the set {x, y}:
7. If M = {multiples of 3 less than 20} and N = {odd numbers less than 15}, write these sets in roster form and find M ∩ N:
M = { _________________ }
N = { _________________ }
M ∩ N = { _________________ }
8. True or False? Check all correct statements:
∅ ⊆ {1, 2, 3}
{5} ∈ {1, 3, 5, 7}
{2, 4} ⊆ {1, 2, 3, 4, 5}
7 ∈ {1, 3, 5, 7}
🎯 Part 3: Problem Solving
9. In a class of 30 students, 18 study Mathematics, 15 study Science, and 8 study both subjects. How many students study neither Mathematics nor Science?
10. Explain the difference between equal sets and equivalent sets using your own examples:
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