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Relations And Functions class 11 Notes Mathematics
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CBSE Class 11 Mathematics
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Chapter – 2
Relations And Functions class 11 Notes Mathematics
- Cartesian Product of Sets
- Relations
- 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
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