# Logic derivation questions?

I need help with the following categorical derivation: (P = ~Q) = ~(P = Q) I can do the first half, although there might be a faster way to do it: 1.....P = ~Q................A. 2........P = Q...............A. 3...........Q..................A. 4...........P = Q...........R:... show more I need help with the following categorical derivation:

(P = ~Q) = ~(P = Q)

I can do the first half, although there might be a faster way to do it:

1.....P = ~Q................A.
2........P = Q...............A.
3...........Q..................A.
4...........P = Q...........R: 2
5...........P..................= E: 3, 4
6...........P = ~Q.........R: 1
7...........~Q...............= E: 5,6
8........~Q..................~I: 3, 7
9........P = ~Q............R: 1
10......P.....................= E: 8, 9
11......Q.....................= E: 2, 10
12...~(P=Q)...............~I: 2, 8, 11

I also have another question:

Can someone help me derive H from the following premise?

~(H > G)

I would appreciate help with either of these questions. They may be very simple, but for some reason I'm having trouble with them.