Question

Cheeck whether the relation R. defined in the set {1,2,3,4,5,6} as R ={(a,b):b=a+1} is reflexive, symmetric or transitive.

Answer 1

Let A ={1,2,3,4,5,6}
A relation R is defined on set A is
R ={a,b: b=a+1}. Therefore, R ={(1,2),(2,3),(3,4),(4,5),(5,6)}
Now, $6ϵAbut(6,6)\text{/}ϵR.$
Therefore, R is not reflexive.
It can be observed that $(1,2)ϵR$ but $(2,1)\text{/}ϵR$. Therefore, R is not symmetric.
Now, $(1,2),(2,3)ϵR$ but $(1,3)\text{/}ϵR$. Therefoe, R is not transitive.
Hence, R is neither reflexive nor symmetric nor transitive.