Let's say I have a statement: if p then q.
The converse would be: if q then p.
The inverse would be: if not p then not q.
The contraposition would be: if not q then not p.
What would you call the following? if not p then q.
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There's no name for it, because there's no real connection between them. The inverse and converse exist because they still assert a direct correlation between p and q; it's just that, as opposed to the regular and contrapositive forms, the condition for failure is reversed.
On the other hand, "if not p then q" is a completely different assertion.
$$ p \Rightarrow q \equiv \lnot p \lor q $$
$$ \lnot p \Rightarrow q \equiv p\lor q $$ It is logically equivalent to "$p$ or $q$"