Question

In the set of natural numbers let R be the relation defined as aRb if and only if a,b belongs to N and a+2b =11 .Write R as the set of ordered pairs .Find the domain and range of R
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Answer 1

$\underline{\textsf{Given:}}$

In N, R is defined by

$\mathsf{_aR_b\,\iff\,a+2b=11}$

$\underline{\textsf{To find:}}$

$\textsf{R, Domain and range of R}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

$\mathsf{1+2(5)=11\,\implies\,_1R_5}$

$\mathsf{3+2(4)=11\,\implies\,_3R_4}$

$\mathsf{5+2(3)=11\,\implies\,_5R_3}$

$\mathsf{7+2(2)=11\,\implies\,_7R_2}$

$\mathsf{9+2(1)=11\,\implies\,_9R_1}$

$\textsf{Then,}$

$\mathsf{R=\{(1,5),(3,4),(5,3),(7,2),(9,1)\}}$

$\textsf{Domain of R}\,\mathsf{=\{1,3,5,7,9\}}$

$\textsf{Range of R}\,\mathsf{=\{1,2,3,4,5\}}$

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Answer 2

Answer:

R = {(9,1),(7,2),(5,3),(3,4),(1,5)} ;

Domain of R = {9,7,5,3,1} ; Range of R = {1,2,3,4,5}