Class 11 Maths - Chapter 1: Sets (Simple Notes)
1. Set
A set is a well-defined collection of objects.
Example: A = {1, 2, 3}
2. Types of Sets
• Finite Set: Number of elements is limited.
• Infinite Set: Number of elements is unlimited.
• Empty Set: No elements, written as {} or ∅.
• Singleton Set: Only one element.
3. Subset
If every element of A is in B, then A ⊆ B.
Proper subset: A ⊂ B (A ≠ B)
4. Universal Set
A set containing all possible elements under discussion.
5. Venn Diagram
Diagram used to represent sets visually.
6. Operations on Sets
• Union (A ∪ B): All elements of A and B
• Intersection (A ∩ B): Common elements
• Difference (A − B): Elements in A not in B
• Complement (A′): Not in A
7. Important Formulas
• n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
8. De Morgan’s Laws
• (A ∪ B)′ = A′ ∩ B′
• (A ∩ B)′ = A′ ∪ B′
1. Set
A set is a well-defined collection of objects.
Example: A = {1, 2, 3}
2. Types of Sets
• Finite Set: Number of elements is limited.
• Infinite Set: Number of elements is unlimited.
• Empty Set: No elements, written as {} or ∅.
• Singleton Set: Only one element.
3. Subset
If every element of A is in B, then A ⊆ B.
Proper subset: A ⊂ B (A ≠ B)
4. Universal Set
A set containing all possible elements under discussion.
5. Venn Diagram
Diagram used to represent sets visually.
6. Operations on Sets
• Union (A ∪ B): All elements of A and B
• Intersection (A ∩ B): Common elements
• Difference (A − B): Elements in A not in B
• Complement (A′): Not in A
7. Important Formulas
• n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
8. De Morgan’s Laws
• (A ∪ B)′ = A′ ∩ B′
• (A ∩ B)′ = A′ ∪ B′
