NOTE: p & q here are logical statements (propositions, having fixed truth values).So in this example of yours
- p: P is unbounded
- q: D is infeasible
'and vice versa' in the language of logic means p <--> q is true, which is actually the case, when both p-->q & q-->p are true. i.e. (truth of p implies truth of q) AND (truth of q implies truth of p).
Hence in your example,
- If P is unbounded, D is infeasible AND
- If D is infeasible, P is unbounded
There're some cases, where 'vice versa' may mean what you doubt it means, like in the following example:
If a proposition is false, it's negation is true & vice versa.
where 'vice versa' seem to imply :-
If proposition is true, it's negation is false OR
- If negation of proposition is true, proposition is false.
So, it pretty much depends on the context in which this's said, since both appear to be logically (!) correct. In your context, you need to mention what P & D actually are (what mathematical structures are they?) , so as to check if D can ever be unbounded or P can ever be infeasible.