# RELATIONS AND FUNCTIONS CLASS 11 MATHS

*In this Chapter, we studied about relations and functions.The main features of this Chapter are as follows:*

*Ordered pair A pair of elements grouped together in a particular order.*

*Cartesian product A × B of two sets A and B is given by A × B = {(a, b): a ∈ A, b ∈ B} In particular R × R = {(x, y): x, y ∈ R} and R × R × R = (x, y, z): x, y, z ∈ R}*

*If (a, b) = (x, y), then a = x and b = y. *

*If n(A) = p and n(B) = q, then n(A × B) = pq. *

*A × φ = φ *

*In general, A × B ≠ B × A.*

*Relation A relation R from a set A to a set B is a subset of the cartesian product A × B obtained by describing a relationship between the first element x and the second element y of the ordered pairs in A × B.*

*The image of an element x under a relation R is given by y, where (x, y) ∈ R,*

*The domain of R is the set of all first elements of the ordered pairs in a relation R.*

*The range of the relation R is the set of all second elements of the ordered pairs in a relation R.*

*Function A function f from a set A to a set B is a specific type of relation for which every element x of set A has one and only one image y in set B. We write f: A→B, where f(x) = y.*

*A is the domain and B is the codomain of f.*

*The range of the function is the set of images. *

*A real function has the set of real numbers or one of its subsets both as its domain and as its range.*

*Algebra of functions For functions f : X → R and g : X → R, we have **(f + g) (x) = f (x) + g(x), x ∈ X **(f – g) (x) = f (x) – g(x), x ∈ X **(f.g) (x) = f (x) .g (x), x ∈ X **(kf) (x) = k ( f (x) ), x ∈ X, where k is a real number.**(f/g) (x) =f(x)/g(x), x ∈ X, g(x) ≠ 0*

- Ordered Pairs
- Cartesian Product
- NCERT Exercise 2.1