🗺️ Chapter Roadmap
1 What is a Set?
In mathematics, a Set is a collection of well-defined and distinct objects.
- Well-defined: Everyone should agree on what belongs in the set (e.g., "Set of vowels" is well-defined, but "Set of beautiful flowers" is NOT).
- Distinct: No object is repeated inside a set.
Standard Notation:
We use Capital Letters to name a set and curly brackets { } to list its members (elements).
2 Important Symbols
3 Types of Sets
🗑️ Empty / Null Set
A set that has no elements at all.
🌍 Universal Set
The "mother set" that contains all elements under consideration.
📦 Subset
If every element of A is also in B, A is a subset of B.
👯 Equal vs Equivalent
Equal: Exactly same members.
Equivalent: Same number of members.
🔥 The Subset Formula (2n)
Examiners often ask: "How many subsets can be formed from a set?" If a set has n elements, use this formula:
Example: If A = {1, 2}, it has 2 elements. Total subsets = 22 = 4.
(Subsets are: { }, {1}, {2}, {1, 2})
4 Set Operations
Let's use two sets: A = { 1, 2, 3 } and B = { 3, 4, 5 }.
Union (A ∪ B)
"Join everything together"
Intersection (A ∩ B)
"Only the common part"
Difference (A − B)
"A minus the part of B"
5 Venn Diagrams Logic
Overlapping Sets
Venn Diagrams use circles to represent sets. The rectangle surrounding the circles is the Universal Set (U).
Formula: A' = U − A