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Q.
The relation $R$ defined in $A =\{1,2,3\}$ by $aRb$, if $\left| a ^{2}- b ^{2}\right| \leq 5$. Which of the following is false?
Relations and Functions - Part 2
Solution:
$R =\{(1,1),(1,2),(2,1),(2,2),(2,3),(3,2),(3,3)\}$
$R ^{-1}=\{( y , x ):( x , y ) \in R \}$
$=\{(1,1),(2,1),(1,2),(2,2),(3,2),(2,3),(3,3)\}= R$
Domain of $R =\{ x :( x , y ) \in R \}=\{1,2,3\}$
Range of $R =\{ y :( x , y ) \in R \}=\{1,2,3\}$