SYMBOLIC LOGIC!! construct an annotated derivation for the argument?

Question

construct an annotated derivation for the arguement
1. (P @ ~Q) > (S > Q)
2. (P > ~Q) @ P
3.~Q > (S V T)
therefor 4. ~Q @ T

Answer 1

I'm going to assume @ is "and", which is more commonly done as &, and that > is implication, commonly →.

1. (P & ~Q) → (S → Q)
2. (P → ~Q) & P
3. ~Q → (S v T)
4. P .... from 2 by simplification
5. P → ~Q .... from 2 by simplificaton
6. ~Q .... from 4 and 5, modus ponens
7. P & ~Q .... from 4 and 6, conjunction
8. S → Q .... from 1 and 7, modus ponens
9. ~S .... from 8 and 6, modus tollens
10. S v T .... from 3 and 6, modus ponens
11. T .... from 10 and 9, disjunctive syllogism (or whatever your book calls it)
12. ~Q & T .... from 6 and 11, conjunction

I used a casual left and right handed simplification. If your teacher is strict, and you can only simplify out the left side of the conjunction, then insert a step that reverses the order with the commutative rule.