Q163 / 270 · NDA 2016 (Phase 2) · Mathematics

Let $R$ be a relation from $A=\{1,2,3,4\}$ to $B=\{1,3,5\}$ such that $R=[(a, b): a \lt b$, where $a \in A$ and $b \in B]$. What is $R_0{ }^{-1}$ equal to?

  • 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

$\mathrm{R}=\{(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\}$ $\begin{aligned} & \Rightarrow \quad \operatorname{R}^{-1}=\{(3,1),(5,1),(3,2),(5,2),(5,3),(5,4)\} . \\ & \Rightarrow \quad \operatorname{RoR}^{-1}=\{(3,3),(3,5),(5,3),(5,5)\} .\end{aligned}$

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

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