Question

If a relation $R$ is defined from a set $A = \{2,3,4,5\}$ to a set $B = \{3,6,7,10\}$ as follows $(x,y) \in R \Leftrightarrow x$ divides $y$. Expression of $R^{-1}$ is represented by

• A. $\{(6,2), (10,2), (3,3), (6,3)\}$
• B. $\{(6,2), (3, 3), (10, 5), (10, 2)\}$
• C. $\{(6,2), (10,2), (3,3), (6,3), (10,5)\}$
• D. None of these

Answer 1

Answer: (C)

Recall that $a/b$ stands for $a$ divides $b$. For the elements of the given sets $A$ and $B$, we find $2/6$, $2/10$, $3/3$, $3/6$, $5/10$
$\Rightarrow R = \{(2,6), (2,10), (3, 3), (3,6), (5,10)\}$
$\therefore R^{-1}= \{(6, 2), (10,2), (3, 3), (6, 3), (10,5)\}$