Using ">" for material implication, (P > Q) is equivalent to each of (~ P v Q) and (Q v ~ P). So you can deduce either of those disjunctions. I think it's just a matter of convention to favor the first of them. The reader is expected to notice the equivalence of the two disjunctions.

Now, (Q v ~ P) is certainly not equivalent to (~ Q v ~ P). From Q, you can infer the first of those disjunctions but not the second. The disjunction (Q v ~ P) is equivalent to (P > Q), whereas the disjunction (~ Q v ~ P) is equivalent to (P > ~ Q) and (Q > ~ P).

## Using ">" for material

Using ">" for material implication, (P > Q) is equivalent to each of (~ P v Q) and (Q v ~ P). So you can deduce either of those disjunctions. I think it's just a matter of convention to favor the first of them. The reader is expected to notice the equivalence of the two disjunctions.

Now, (Q v ~ P) is certainly not equivalent to (~ Q v ~ P). From Q, you can infer the first of those disjunctions but not the second. The disjunction (Q v ~ P) is equivalent to (P > Q), whereas the disjunction (~ Q v ~ P) is equivalent to (P > ~ Q) and (Q > ~ P).