SOLUTION: Prove that the argument is valid using the method of natural deduction. tilde (Q horseshoe tilde R) tilde (tilde P dot Q) / therefore tilde R horseshoe (P dot Q)

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Question 1208944: Prove that the argument is valid using the method of natural deduction.
tilde (Q horseshoe tilde R)
tilde (tilde P dot Q) / therefore tilde R horseshoe (P dot Q)
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!

Here's one way to do the derivation. Interestingly, premise #2 is never used so I don't know if I might have overlooked something or perhaps your teacher made a typo somewhere.
I'm using an arrow in place of a horseshoe.
Also, I'm using an ampersand (&) in place of a dot.

Number Statement Line(s) Used Reason
1 ~(Q --> ~R)
2 ~(~P & Q)
:. ~R --> (P & Q)
3 ~(~Q v ~R) 1 Material Implication
4 ~(~Q) & ~(~R) 3 De Morgan’s Law
5 Q & R 4 Double Negation
6 R & Q 5 Commutation
7 R 6 Simplification
8 R v (P & Q) 7 Addition
9 ~R --> (P & Q) 8 Material Implication

Here's a list of rules of inference and replacement