Example 7:

Example 7:-  Let A=, {1,2,3,4,5,6}. Define a relation R from A to A by R={(x,y):y=x+1}
(i) Depict this relation using an arrow diagram.
(ii) Write down the domain, codomain the range of R. 

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{A}=\left\{1,2,3,4,5,6\right\} \\ \mathrm{R}=\left\{\left(\mathrm{x},\mathrm{y}\right): \mathrm{y}=\mathrm{x}+1\right\} \mathrm{and} \mathrm{both} \mathrm{x},\mathrm{y}\in \mathrm{A} \\ \mathrm{Codomain} \mathrm{is} \mathrm{set} \mathrm{A} \mathrm{itslef}. \\ \mathrm{For} \mathrm{y}=\mathrm{x}+1 ,\mathrm{when} \\ \mathrm{x}=1, \mathrm{y}=2 \\ \mathrm{when} \mathrm{x}=2 \\ \mathrm{y}=3 \\ \mathrm{when} \mathrm{x}=3 \\ \mathrm{y}=4 \\ \mathrm{when} \mathrm{x}=4 \\ \mathrm{y}=5 \\ \mathrm{when} \mathrm{x}=5 \\ \mathrm{y}=6 \\ \mathrm{when} \mathrm{x}=6 \\ \mathrm{y}=7 \mathrm{but} 7 \mathrm{does} \mathrm{not} \mathrm{belong} \mathrm{to} \mathrm{A} \\ \mathrm{Hence} \\ \mathrm{Domain} \mathrm{is} \left\{1,2,3,4,5\right\} \\ \mathrm{Range} \mathrm{is} \left\{2,3,4,5,6\right\} \\ \mathrm{R}=\left\{\left(1,2\right),\left(2,3\right),\left(3,4\right),\left(4,5\right), \left(5,6\right)\right\} \\ \left(\begin{array}{c}1\\ 2\\ 3\\ 4\\ 5\end{array}\right)\begin{array}{c}\to \\ \to \\ \to \\ \to \\ \to \end{array}\left(\begin{array}{c}2\\ 3\\ 4\\ 5\\ 6\end{array}\right) \end{gathered}$$

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