Definitions [4]
Definition: Two sets A and B are said to be equal if they have exactly the same elements and we write A = B. Otherwise, the sets are said to be unequal and we write A ≠ B.
A 'set A' is said to be a subset of a set B if every element of A is also an element of B.
The union of two sets A and B is the set C which consists of all those elements which are either in A or in B (including those which are in both). In symbols, we write. A ∪ B = {x : x ∈A or x ∈B}
The intersection of two sets A and B is the set of all those elements which belong to both A and B. Symbolically, we write A ∩ B = {x : x ∈ A and x ∈ B}
Key Points
Key Points: Venn Diagram
| Logical Form | Set Form |
|---|---|
| p ∧ q | A ∩ B |
| p ∨ q | A ∪ B |
| ∼p | A′ (complement) |
| p → q | A ⊂ B |
| p ↔ q | A = B |
Concepts [17]
- Sets and Their Representations
- Classification of Sets
- Empty Set (Null or Void Set)
- Finite and Infinite Sets
- Equal Sets
- Subsets
- Power Set
- Universal Set
- Venn Diagrams
- Union of Sets
- Intersection of Sets
- Disjoint Sets
- Difference of Sets
- Complement of a Set
- Practical Problems on Union and Intersection of Two Sets
- Algebra of Real Functions
- Algebraic Operations on Functions
