Class 11th Mathematics - Sets and Relations

Sets and Relations - Class 11th Mathematics

Sets and relations form the foundation of modern mathematics and are essential for higher studies.

Sets

A set is a collection of well-defined objects called elements.

• Roster Method: A = {1, 2, 3, 4, 5}
• Set Builder Method: A = {x : x is a natural number and x ≤ 5}

Types of Sets

• Finite Set: Contains countable number of elements
• Infinite Set: Contains uncountable number of elements
• Empty Set: Contains no elements (φ or {})
• Universal Set: Contains all elements under consideration

Set Operations

• Union (A ∪ B): Elements in A or B or both
• Intersection (A ∩ B): Elements common to both A and B
• Difference (A - B): Elements in A but not in B
• Complement (A'): Elements not in A

Relations and Functions

• Relation: A subset of A × B
• Function: A relation where each element of domain has unique image
• Domain: Set of all first elements
• Range: Set of all second elements

Practice Problems

1. If A = {1, 2, 3} and B = {2, 3, 4}, find A ∪ B and A ∩ B.
2. Determine if f(x) = x² is a function from R to R.
3. Find the domain and range of f(x) = 1/(x-2).