Hi everyone, does anyone know what the solutions to these questions would be? I am really struggling with this particular piece of homework, so would appreciate any help or explanations. I have to prove that the following statements are valid in proven logic. Thank you

¬ = not → = if/ then

¬ ¬(P & Q) : ¬ ¬ (Q & P) (6)

¬ P → ¬Q: Q → P (6)

: (P →Q) → (¬Q →¬P) (5) Principle of transposition

Q → R : (¬Q →¬P) →(P →R) (9)

(P & Q) →¬R : R →(P →¬Q) (11)

P: [(¬(Q → R) →¬P)] →[( ¬R →¬Q)] (9)

P, ¬Q: ¬ (P →Q) (6)

P, ¬P : Q (8)

: ¬P → (P →Q) (10) Law of Dun Scotus

P → ¬P : ¬P (11)