# The binary relation $S=\phi$ on set $A=\{1,2,3\}$

I came across this question:

The binary relation $S=\phi$ (empty set) on set $A=\{1,2,3\}$ is

a) Neither reflexive nor symmetric
b) Symmetric and reflexive
c) Transitive and refelxive
d) Transitive and symmetric

Please tell me if my understanding is correct:

For example, let $A=\{1,2,3\}$ then $A\times A=\{(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3)\}$

and we are asked to do something as $1S1,1S2$...etc?

This is as far as I can understand it

Hint Go back to the definitions:

$S$ is reflexive iff for every $x\in A$, we have $(x,x)\in S$. Since there are no pairs $(a,b)\in S$, what can you conclude?

$S$ is symmetric iff whenever $(x,y)\in S$ then $(y,x)\in S$. Since there are no pairs $(x,y)\in S$, what can you conclude?

$S$ is transitive iff ... . What can you conclude?