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Question: Answered & Verified by Expert
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
MathematicsSets and RelationsVITEEEVITEEE 2011
Options:
  • A $\{(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\}$
  • B $\{(3,1),(5,1),(3,2),(5,2),(5,3),(5,4)\}$
  • C $\{(3,3),(3,5),(5,3),(5,5)$
  • D $\{(3,3),(3,4),(4,5)\}$
Solution:
2852 Upvotes Verified Answer
The correct answer is: $\{(3,3),(3,5),(5,3),(5,5)$
$\quad \mathrm{A}=\{1,2,3,4\}$ and $\mathrm{B}=\{1,3,5\}$ $\therefore \mathrm{R}=\{(1,3),(1,5),(2,3),(2,5),(3,5),(4,$, and $\mathrm{R}^{-1}=\{(3,1),(5,1),(3,2),(5,2),(5)$ $(5,4)\}$ $\therefore \mathrm{ROR}^{-1}=\{(3,3),(3,5),(5,3),(5,5)\}$

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