Suppose S is the following relation on the set of integers:
m S n if, and only if, 9 | (m^2 – n^2 + 6)

Is the set not reflexive, not symmetric and not transitive?

Question

Suppose S is the following relation on the set of integers:
m S n if, and only if, 9 | (m^2 – n^2 + 6)

Is the set not reflexive, not symmetric and not transitive?

anonymous · Answer

Do it one property at a time.  Do you know w hat the reflexive property is?

anonymous · Answer

Also, it's not the set which has properties, it is the relation which has properties.

anonymous · Answer

reflexive : $mSn\implies nSm$ which in this case means $9|m^2-n^2+6\implies 9|n^2-m^2+6$

anonymous · Answer

@satellite73 That's symmetric property.
Reflex is the case that $nSn$ is true for all $n$.

anonymous · Answer

oops

anonymous · Answer

@wio  is correct, that is symmetric