Question

If $R$ is a relation from $\{11,12,13\}$ to $\{8,10,12\}$ defined by $y=x-3$. Then, $R^{-1}$ is equal to

• A. $\{(8,11),(10,13)\}$
• B. $\{(11,18),(13,10)\}$
• C. $\{(10,13),(8,11)\}$
• D. None of these

Answer 1

The correct option is A

$\{(8,11),(10,13)\}$

Explanation for the correct option:

Thr relation $R$ is given by $y=x-3$

if $x=11\to y=11-3=8$

if $x=12\to y=12-3=9$

if $x=13\to y=13-3=10$

Then from the relation $R$ the ordered pairs obtain are $\{(11,8),(13,10)\}$

Neglect the pair $(12,9)$ as it does not belongs to the given set.

Therefore, the inverse of $R$ is $R^{-1}=\{(8,11),(10,13)\}$.

Hence, the correct option is (A).