Question

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

• A. $(11,8)\in R^{-1}$
• B. $(10,13)\in R$
• C. $(10,13)\in R^{-1}$
• D. $(11,8)\in R$

Answer 1

Answer: (C), (D)

The correct options are
C $(10,13)\in R^{-1}$
D $(11,8)\in R$

$R$ is a relation from $\{11,12,13\}$ to $\{8,10,12\}$ defined by $y=x-3\Rightarrow x-y=3$
Therefore, $R=\left\{\right(11,8),(13,10\left)\right\}$
Hence, $R^{-1}=\left\{\right(8,11),(10,13\left)\right\}$