properties of relations I'm trying to do some chapter problems on equivalence relations. I'm stuck in the second section "properties of relations."
Question: Let $A=\{a,b,c,d\}$. Give an example of a relation $R$ on $A$ that is neither reflexive, symmetric ,or transitive.
What I tried doing was writing out all the pairs and then canceling out the ones that matched with the laws.  I was left with $\{(d,b) (d,c)\}$. Does that mean $R=\{(d,b) (d,c)\}$ is not reflexive, transitive, or symmetric ?

Well, the relation you give is indeed neither reflexive nor transitive, but there are many ways to get such a relation.  "Cancelling out pairs that don't match the laws" is not a well defined procedure.  (Well, it is defined for reflexivity, but it does not do what you want:  You would be left with $\{(a,a),(b,b),(c,c),(d,d)\}$ which is reflexive). 
I think the problem would like you to find a relation that involves all four of the members of the set.  You could, for example, add in $(a,b)$.  Or even $(a,a)$; just one element being equivalent to itself does not make the relation reflexive if others are not.
