SETS AND RELATIONS - Short Notes
SETS
A set is a well-defined collection of distinct objects called elements.
Representation: Roster form and Set-builder form.
Types: Empty set, Finite set, Infinite set, Equal sets, Subsets.
Operations: Union, Intersection, Difference, Complement.
Laws: Commutative, Associative, Distributive laws.
RELATIONS
A relation from A to B is a subset of Cartesian product A × B.
Cartesian Product: A × B = {(a, b)}
Types: Reflexive, Symmetric, Transitive.
Equivalence Relation: Reflexive + Symmetric + Transitive.
FUNCTIONS
A function is a relation where each input has exactly one output.
Types: One-One, Onto, Bijective.
Terms: Domain, Codomain, Range.
SETS
A set is a well-defined collection of distinct objects called elements.
Representation: Roster form and Set-builder form.
Types: Empty set, Finite set, Infinite set, Equal sets, Subsets.
Operations: Union, Intersection, Difference, Complement.
Laws: Commutative, Associative, Distributive laws.
RELATIONS
A relation from A to B is a subset of Cartesian product A × B.
Cartesian Product: A × B = {(a, b)}
Types: Reflexive, Symmetric, Transitive.
Equivalence Relation: Reflexive + Symmetric + Transitive.
FUNCTIONS
A function is a relation where each input has exactly one output.
Types: One-One, Onto, Bijective.
Terms: Domain, Codomain, Range.
