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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 set$R=\left(1,2\right),\left(–2,3\right),\left(\frac{1}{2},3\right)$ is a relation; the domain of $R=\left\{1,–2,\frac{1}{2}\right\}$ and the range of $R=\left\{2,3\right\}$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 $f:X\to Y$ 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 $x\in X,$ there is a unique element $yinY$ that is related to $x$. The unique element $y$ to which $f$ relates $x$ is denoted by $f\left(x\right)$ 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 of$f\left(x\right)$ taken together is called the range of $f$ or image of $X$ under $f$. Symbolically. range of $f=\left\{y\in Y|y=f\left(x\right),forsomexinX\right\}$

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