/sci/ - Science & Math

this is the given solution to one of a group of exercises in an intro to logic book im reading, where the goal is to use elimination of synonyms, conversion/obversion/contraposition, and uniform translation to translate arguments to (not necessarily valid) standard form categorical syllogisms. this solution doesn't make sense to me.
ignore the content of the arguments. the solution is invalid, which doesnt matter.


Exercise:

All syllogisms having two negative premises are invalid.

Some valid syllogisms are sound.

Therefore, some unsound arguments are syllogisms having two negative premises.
Solution:

No syllogisms having two negative premises are valid syllogisms.

Some valid syllogisms are not unsound arguments.

Therefore, some unsound arguments are syllogisms having two negative premises.


To get from the exercise to the solution, you have to obvert both premises, and only then apply the parameters "syllogisms" and "arguments". How is this a solution? how can you take the compliments of "invalid" and "sound", and only then apply those specific parameters? If you try to apply the parameters before obversion, it doesn't work, because the compliments of "sound arguments" and "invalid syllogisms" are different than those of the adjectival terms themselves. Isn't applying these parameters to these terms only after taking their compliments denying that the terms mean what you acted as though they did in order to get their compliments?