$R_{1}=\{(a, b) \in N \times N:|a-b| \leq 13\}$

$R_{2}=\{(a, b) \in N \times N:|a-b| \neq 13\}$.

For $R_{1}$ :

$(i)\,Reflexive \,\,relation$

$(a, a) \in N \times N:|a-a| \leq 13$

$(ii)\, Symmetric\,\, relation$

$( a , b ) \in R _{1},( b , a ) \in R _{1}:| b – a | \leq 13$

$(iii) \,Transitive\, \,relation$

$( a , b ) \in R _{1},( b , c ) \in R _{1},( a , c ) \in R _{1}:$

$(1,3) \in R _{1,}(3,16) \in R _{1,} \text { but }(1,16) \notin R _{1}$

For $R _{2}$ :

$(i) \,Reflexive\,\, relation$

$(a, a) \in N \times N:|a-a| \neq 13$

$(ii)\, Symmetric\,\, relation$

$(b, a) \in N \times N:|b-a| \neq 13$

$(iii)\, Transitive \,\,relation$

$( a , b ) \in R _{2},( b , c ) \in R _{2},( a , c ) \in R _{2}$

$(1,3) \in R _{2,}(3,14) \in R _{2} \text { but }(1,14) \notin R _{2}$