What is Set/Sets Operations/Types of Sets/Representation of Sets/Venn Diagram/Union/Intersection

1. What is a Set? A set is a well-defined collection of objects called elements 👉 Example: 📘 2. Types of Sets 1. Empty Set or Null Set A set with no elements. Symbol: ∅ 2. Finite Set A set with limited elements. 3. Infinite Set A set with unlimited elements. 4. Equal Sets Two sets with exactly same elements. 5. Subset If all elements of A are in B, then 6. Universal Set The set that contains all possible elements in a discussion. 📘 3. Set Operations 🔹 1. Union of Sets All elements from both sets with no repetition 👉 🔹 2. Intersection of Sets Common elements in both sets 👉 🔹 3. Difference of Sets Elements in A but not in B 👉 👉 🔹 4. Complement of a Set Elements in universal set but not in A 👉 A′ = U − A 🔹 5. Symmetric Difference Elements in A or B but not in both 📘 4. Important Formulas 🔹 Number of Elements If n of A = number of elements in set A Union Formula: 📘 5. Venn Diagrams Venn diagrams are used to visually represent sets and their operations using circles. 👉 Helps to understand: Union Intersection Complement 📘 7. Applications of Sets Probability Statistics Computer Science Logic and reasoning Database systems ✅ Summary A set is a collection of elements Main operations: Union, Intersection, Difference, Complement Use formulas to solve numerical problems Venn diagrams help visualize relationships