Proving logic

Mia fuller

New member
Joined
Mar 5, 2017
Messages
1
Hi everyone, does anyone know how you would work out 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 logic. The numbers in brackets at the side represent how many lines the answer should be. It's taken from Paul tomassi's 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)





 
Hi everyone, does anyone know how you would work out 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 logic. The numbers in brackets at the side represent how many lines the answer should be. It's taken from Paul tomassi's logic. Thank you :)
¬ = not → = if/ then

1. ¬ ¬(P & Q) : ¬ ¬ (Q & P) (6)
2. ¬ P → ¬Q: Q → P (6)
3. : (P →Q) → (¬Q →¬P) (5) Principle of transposition
4. Q → R : (¬Q →¬P) →(P →R) (9)
5. (P & Q) →¬R : R →(P →¬Q) (11)
6. P: [(¬(Q → R) →¬P)] →[( ¬R →¬Q)] (9)
7. P, ¬Q: ¬ (P →Q) (6)
8. P, ¬P : Q (8)
9. : ¬P → (P →Q) (10) Law of Dun Scotus
10. P → ¬P : ¬P (11)
Please reply with a clear listing of your thoughts and efforts so far. When you reply, please explain the "colon" notation, especially as used in exercises (3) and (8) above. (In its other appearances, I suspect it means something along the lines of "such that". Please confirm or correct.) Also, please explain the parenthetical numbers and the phrases that follow the exercise statements.

Thank you! ;)
 
Top