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) reflexive ii)transitative
iii)symmetric

Answer 1

Answer:

Let's write the function in roster form. if I've got the question correctly, then the relation is x+y=10

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

Now, ¥ a€R, (a,a) not€ R. [No (1,1),(2,2)...only (5,5)]. So R is not reflexive.

Now, ¥ (a,b)€R, (b,a)€R [(1,9)-(9,1), (2,8)-(8,2)......]. So R is symmetric.

Now, R is not transitive as there doesn't exist any c such that if ¥ (a,b)€R and (b,c)€R, there could be any (a,c)€R.