Question

let R be a relation of A ={1,2,3,4,5,6,7} given by R ={(a,b)/a-b is divisible by 5}
i) write R in roster form
ii) find its domain & range
iii) Is it a function​

Answer 1

$\textbf{Given:}$

$R\,\text{on}\;A=\{1,2,3,4,5,6,7\}\,\text{by}$

$R=\{(a,b)/\text{a-b is divisible by 5}\}$

$\textbf{To find:}$

$1.\text{Roaster form of R}$

$2.\text{Domain and range of R}$

$3.\text{Is R a function or not}$

$\textbf{Solution:}$

$\text{Consider,}$

$R=\{(a,b)/\text{ a-b is divisible by 5}\}$

$\textbf{Roaster form of R:}$

$R=\{(1,1),(2,2),(3,3),(4,4),(5,5),(6,6),(7,7),(1,6),(6,1),(2,7),(7,2)}$

$\textbf{Domain}=\{1,2,3,4,5,6,7\}$

$\textbf{Range}=\{1,2,3,4,5,6,7\}$

$\text{Also, R is not a function}$

$\text{because 1 and 2 are related to more than one element}$

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