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Describe Relations And Functions


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Relation - A relation R from a non-empty set B is a subset of the cartesian product A×B. For example, the setR=(1,2),(2,3),(12,3) is a relation; the domain of R=1,2,12 and the range of R=2,3

Functions - A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B. In other words, no two distinct elements of B have the same pre-image.

The notation f:XY means that f is a function from XtoY. X is called the domain of fandY is called the co-domain of f. Given an element xX, there is a unique element yinY that is related to x. The unique element y to which f relates x is denoted by f(x) and is called f of x, or the value of f at x, or the image of x under f. The set of all values off(x) taken together is called the range of f or image of X under f. Symbolically. range of f=yY|y=f(x),forsomexinX


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