Question

Construct a relation on the set {a, b, c, d} that is a. reflexive, symmetric, but not transitive

Answer 1

Consider the set $\{a,b,c,d\}$ . Consider the relation.

$R=\{(a,a),(b,b),(c,c),(d,d),(a,b),(b,a),(a,c),(c,a),(b,c),(c,b),(b,d),(d,b)\}$

We can see that the relation is reflexive since every element of the set are related to themselves.

Also it is symmetric for every $aRb,bRa$ and so on.

But, it is not transitive. We have $(a,b)$ and $(b,d)$ but no $(a,d)$