Relations And Functions class 11 Notes Mathematics

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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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CBSE Class-11 Revision Notes and Key Points

The Relations And Functions class 11 Notes Mathematics. CBSE quick revision note for class-11 Mathematics, Physics, Chemistry, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.

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