Let R1 = (a, b) [] N [] N : |a - b| [] 13 and R2 = (a, b) [] N [] N : |a - b| [] 13.

Question

Let R1 = {(a, b) $$\in$$ N $$\times$$ N : |a - b| $$\le$$ 13} and

R2 = {(a, b) $$\in$$ N $$\times$$ N : |a - b| $$\ne$$ 13}. Then on N :

Accepted Answer

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

$R_{2}=\{(a, b) \in N 	imes N:|a-b| 
eq 13\}$

In $R_{1}: \because|2-11|=9 \leq 13$

$	herefore \quad(2,11) \in R_{1}$ and $(11,19) \in R_{1}$ but $(2,19) 
otin R_{1}$

$	herefore \quad R_{1}$ is not transitive

Hence $R_{1}$ is not equivalence

In $R_{2}:(13,3) \in R_{2}$ and $(3,26) \in R_{2}$ but $(13,26) 
otin R_{2}$

$(\because|13-26|=13)$

$	herefore R_{2}$ is not transitive

Hence $R_{2}$ is not equivalence.

Solutions · 1