Let R _{1}={( a , b ) in N times N :| a - b | | vedclass

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Question

$R_{1}=\{(a, b) \in N 	imes N:|a-b| \leq 13\}$

$R_{2}=\{(a, b) \in N 	imes N:|a-b| 
eq 13\}$.

For $R_{1}$ :

$(i)\,Reflexive \,\,relation$

Vedclass · Accepted Answer

Neither $R_{1}$ nor $R_{2}$ is an equivalence relation.

Vedclass · Answer

$R_{1}=\{(a, b) \in N 	imes N:|a-b| \leq 13\}$

$R_{2}=\{(a, b) \in N 	imes N:|a-b| 
eq 13\}$.

For $R_{1}$ :

$(i)\,Reflexive \,\,relation$

$(a, a) \in N 	imes N:|a-a| \leq 13$

$(ii)\, Symmetric\,\, relation$

$( a , b ) \in R _{1},( b , a ) \in R _{1}:| b - a | \leq 13$

$(iii) \,Transitive\, \,relation$

$( a , b ) \in R _{1},( b , c ) \in R _{1},( a , c ) \in R _{1}:$

$(1,3) \in R _{1,}(3,16) \in R _{1,} 	ext { but }(1,16) 
otin R _{1}$

For $R _{2}$ :

$(i) \,Reflexive\,\, relation$

$(a, a) \in N 	imes N:|a-a| 
eq 13$

$(ii)\, Symmetric\,\, relation$

$(b, a) \in N 	imes N:|b-a| 
eq 13$

$(iii)\, Transitive \,\,relation$

$( a , b ) \in R _{2},( b , c ) \in R _{2},( a , c ) \in R _{2}$

$(1,3) \in R _{2,}(3,14) \in R _{2} 	ext { but }(1,14) 
otin R _{2}$

Let $R _{1}=\{( a , b ) \in N \times N :| a - b | \leq 13\}$ and $R _{2}=\{( a , b ) \in N \times N :| a - b | \neq 13\} .$ Thenon $N$

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