Proving logic
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)
¬ = 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)
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