Question

42. A relation R is defined on the set of positive integers as xRy if 2x + y = 5. The
relation Ris
(A) reflexive
(B) transitive
(C) symmetric
(D) not transitive
3.​

Answer 1

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

Relation R is defined by xRy iff 2x+y=5

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

$\textsf{The most appropriate option in the given alternatives}$

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

$\textsf{Consider,}$

$\mathsf{2(1)+3=5\;\implies\;_1R_3}$

$\mathsf{2(2)+1=5\;\implies\;_2R_1}$

$\textsf{Then,}$

$\mathsf{R=\{(1,3),(2,1)\}}$

$\text{But}\;\mathsf(2,1),(1,3)\,\in\,R\implies\,(2,3)\,\notin\,R}$

$\textsf{Hence R is not transitive}$

$\therefore\textsf{Option (D) is correct}$

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