SOLUTION: 1. (J > O) > ~N 2. N v [~N > (E > N)] 3. ~E > [E v (N v ~O)] 4. J > U Conclusion: ~O Can anybody please finish this proof for me? I'm lost.

Im pretty sure the U in 4 should be O, because U does not 
appear anywhere else, so if it were J > U, it might as well have 
been eliminated, as it could play no possible role in the
proof.  So I am going to assume the U is a typo and should 
be O instead.  Then the proof is fairly straight-forward.

1. (J > O) > ~N
2. N v [~N > (E > N)]
3. ~E > [E v (N v ~O)]
4. J > O
Conclusion: ~O

5. ~N             1,4, MP
6. ~N > (E > N)   2,5, DS
7. E > N          6,5, MP
8. ~E             7,5, MT 
9. E v (N v ~O)   3,8, MP
10. N v ~O        9,8, DS
11. ~O           10,5, DS

Edwin