Question

Given s=(1,2,3,4,5,6,7,8,9,10)and a relation r on a where r=(x,y)x+y=10........find whether r has the following properties or not?
I

Answer 1

Answer:

In roster form, R= {(1,9),(2,8),(3,7),(4,6),(5,5),(6,4),(7,3),(8,2),(9,1)}

Clearly, no (1,1), (2,2).... except (5,5). Hence, ¥a€R, (a,a)not€R. So, R is not reflexive.

Now, ¥ (a,b)€R, (b,a)€R. So, R is symmetric.

However, no c exists such that ¥(a,b)€R and (b,c)€R, there could be (a,c)€R. So, R is not transitive.