Question 981965: 1. Q > ~Q
2. ~(G & Q) > U
/ ~(G & ~U)
Can somebody solve this proof please? Thank you :)
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! You can do a proof by contradiction.
Step 1) assume the complete opposite of the conclusion. Assume (G & ~U)
Step 2) Use simplification to get ~U
Step 3) Use modus tollens with line 2 and ~U to get ~~(G & Q) which turns into (G & Q)
Step 4) Simplification frees up Q
Step 5) Modus ponens on line 1, and using the freed up Q from step 4, consequently frees up ~Q
Step 6) We have Q and ~Q they conjunct to (Q & ~Q) which is always false. This is a contradiction.
Since we have a contradiction, the initial assumption (G & ~U) is false which makes the opposite true. That proves ~(G & ~U) is a proper conclusion.
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