Set Theory

Description:
Set theory is the study of collections of objects called sets. It forms the foundation of modern mathematics and is widely used in logic, computer science, and probability.

Key Concepts:

1. Set: A collection of distinct objects.
   • Example: A = {1, 2, 3, 4}
2. Types of Sets:
   • Finite & Infinite: {1,2,3} vs {1,2,3,…}
   • Empty Set: ∅ (no elements)
   • Universal Set: U (all possible elements)
   • Subset: A ⊆ B → every element of A is in B
   • Proper Subset: A ⊂ B → A ⊆ B but A ≠ B
   • Power Set: P(A) = set of all subsets of A
3. Operations on Sets:
   • Union: A ∪ B → elements in A or B or both
   • Intersection: A ∩ B → elements common to A and B
   • Difference: A – B → elements in A but not in B
   • Complement: A’ → elements not in A
4. Venn Diagrams: Visual representation of sets and operations.

Example Problem:
If A = {1,2,3}, B = {2,3,4}, find:

• A ∪ B = {1,2,3,4}
• A ∩ B = {2,3}
• A – B = {1}