If R s a relation defined on set

Question:

If $R$ s a relation defined on set $A=\{1,2,3\}$ by the rule $\left(a_{t} b\right) \in R \Leftrightarrow\left|a^{2}-b^{2}\right| \leq 5$, then $R^{-1}=$

Solution:

Given: $R=\left\{(a, b):\left|a^{2}-b^{2}\right| \leq 5\right\}$, where $A=\{1,2,3\}$ and $a, b \in A$.

R = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 2), (3, 3)}

Therefore, $R^{-1}=\{(1,1),(2,1),(1,2),(2,2),(3,2),(2,3),(3,3)\}=R$

Hence, if $R$ is a relation defined on set $A=\{1,2,3\}$ by the rule $(a, b) \in R \Leftrightarrow\left|a^{2}-b^{2}\right| \leq 5$, then $R^{-1}=\underline{R}$.

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