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?

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

oops

Answer 6

@wio is correct, that is symmetric