Hello I need help proving these Logic Problems. I've solved most of them but I would like to see what you guys come up with. I am supposed to use the Laws of Sentential Logic and Inference Rules.

Given p, (p → q) and (q → r), prove r.

Given (p ↔ q) and p, prove q.

Given (p∧q) and (p → s), prove s.

Given (¬p → q), ¬q prove p.

Given (p ∨ q) and ¬q prove (p ∨ s).

• Given (p ∨ (q ∧ F)) and (p → q) prove q.