If R be a relation from A=\1,2,3,4\ to B=\1,3,5\ such that (a, b) ∈ R ⇔ a < b , then ROR^-1 is

Correct answer: (C) \(3,3),(3,5),(5,3),(5,5). A=\1,2,3,4\ and B=\1,3,5\ ∴ R=\(1,3),(1,5),(2,3),(2,5),(3,5),(4, , and R^-1=\(3,1),(5,1),(3,2),(5,2),(5) (5,4)\ ∴ ROR^-1=\(3,3),(3,5),(5,3),(5,5)\

Q42 / 120 · VITEEE 2011 · Mathematics

If $\mathrm{R}$ be a relation from $A=\{1,2,3,4\}$ to $B=\{1,3,5\}$ such that $(a, b) \in \mathrm{R} \Leftrightarrow a < b$, then $\mathrm{ROR}^{-1}$ is

A
$\{(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\}$
B
$\{(3,1),(5,1),(3,2),(5,2),(5,3),(5,4)\}$
Correct answer
C
$\{(3,3),(3,5),(5,3),(5,5)$
D
$\{(3,3),(3,4),(4,5)\}$

Solution

$\quad \mathrm{A}=\{1,2,3,4\}$ and $\mathrm{B}=\{1,3,5\}$ $\therefore \mathrm{R}=\{(1,3),(1,5),(2,3),(2,5),(3,5),(4,$, and $\mathrm{R}^{-1}=\{(3,1),(5,1),(3,2),(5,2),(5)$ $(5,4)\}$ $\therefore \mathrm{ROR}^{-1}=\{(3,3),(3,5),(5,3),(5,5)\}$

Hence, the correct answer is option: 'C'.

If $\mathrm{R}$ be a relation from $A=\{1,2,3,4\}$ to $B=\{1,3,5\}$ such that $(a, b) \in \mathrm{R} \Leftrightarrow a < b$, then $\mathrm{ROR}^{-1}$ is

Solution

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