are these binary relations?

Question

I have found the following examples of Binary Relations, but I am not pretty sure is the conclusion the author arrived is correct.

X is a number of people

x N y, implies that x lives next to y; for what I see this does not hold the transitive property, so it is not a binary relation, but the author says so? am I wrong?

x S y, x is a sister of y; this example does not hold the symmetric property, but I found the author says it is a binary one, is that right?

thanks

Answer 1

Binary relations on X are just sets N$\subseteq$X$^2$. They don't have to be transitive.