Soundness and Completeness of a limited language

[SynodOfDordt]

I was challenged with completing this task.

"Consider languages whose logical vocabulary is restricted to just negation and contradiction/absurdity/bottom. Thus, conjunction, disjunction, implication etc. do not occur in sentences of these languages. We can still conduct proofs for such languages using the following natural deduction rules:
(negation-introduction, negation-elimination, double negation-elimination). With regard to languages restricted in this way, complete the
following tasks:

(1) Show that the fragment of the natural deduction system is sound.
(2) Show that the fragment of the natural deduction system is complete (massage the
statement, get a special set, define a model and show it has the desired properties).
(3) Now imagine that we do not allow double negation-elimination as a rule. Do we still have soundness?
Do we still have completeness? If not, identify where the attempted proof of that
fact would break down."

Any insights would be appreciated

[Dalek Prime]

Did you ever complete it? Sounds like you wanted someone to do your homework for you.