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CBSE Guide Relations And Functions class 11 Notes

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Relations And Functions class 11 Notes Mathematics

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CBSE Class 11 Mathematics
Revision Notes
Chapter – 2
Relations And Functions class 11 Notes Mathematics

1. Cartesian Product of Sets
2. Relations
3. Functions

•  Ordered pair  A pair of elements grouped together in a particular order. Clearly, .

• Cartesian product 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: 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, i.e., .
• Number of Relations: Let A and B be two non-empty finite sets, comtaining m and n elements respectively, then the total number of relaitons from A to B is
• Domain: The domain of R is the set of all first elements of the ordered pairs in a relation R. Domain R = .

• The image of an element x under a relation R is given by y, where (x, y) ∈ R,
• Range: The range of the relation R is the set of all second elements of the ordered pairs in a relation R. Range R = .
• Function: 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.
• Domain and Co-domain: The set A is called the domain of function f and the set B is called the co-domain of f.
• Range: If f is a function from A to B, then each element of A corresponds to ine and only one element of B, whereas every element in B need not be the image of some  in A. The subset of B comtaining the image of elements of A is called the range of the function. The range of f is denoted by . Mathematically, we write:
• Image: If the element x of A corresponds to  under the function f, then we say that  is the image of  under f and we write, .
• Pre-image: If , then  is pre-image of

The Relations And Functions class 11 Notes

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