Question 981965
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.