If and only if

pfjddream

For statements with if and only if, does it matter which variable I write first?

Example: V is selected if and only if P is selected

the if and only if here is referring to P so the solutions in the book show

P <--> V
not V <--> not P

but if I wrote it out as

V <--> P
not P <--> not V

Would that be correct since this is a biconditional statement? if past would make P sufficient condition and the only if part would make P the necessary condition. Am I thinking of this correctly?

Also, can I think of biconditionals as implying that the two variable must always go together meaning that PV will always be together in the "in" group or in the "out" group. There is never a possibilities where one variable is in and the other is out. So, I could show them as a block in my diagram.