Logical meaning of "vice versa"? I was wondering what "vice versa" means using the language of logic?


*

*For example,

If P is unbounded, D is infeasible, and vice versa.

Does the vice versa part mean that
"If D is infeasible, P is unbounded", "If D is unbounded, P is
infeasible", or something else?

*How to understand "vice versa"
generally?


Thanks!
 A: 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.
A: For all future readers who want a concise answer. 
Vice versa means the converse/inverse of the statement. 
The inverse is logically equivalent to the converse of the statement. However, one cannot assume the inverse is true. The inverse is the contrapositive of the converse of the original statement.
If P then Q is a conditional statement. 
If Q then P is the converse.
If -P then -Q is the inverse of the conditional statement, which is logically equivalent to the converse, but is the contrapositive of the converse.
Example:
 This is seen is baby Rudin. In the proposition 1.18 
a) if x>0 then -x <0, and vice versa.
