# 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:...
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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.

Thanks in advance

(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.

Thanks in advance

Update:
Thank you Tim. To clarify, = stands for a biconditional, so I'm not affirming the consequent where you thought I was. Here is a list of the symbols I use:

~: negation

&: conjunction

v: disjunction

>: conditional

=: biconditional

~: negation

&: conjunction

v: disjunction

>: conditional

=: biconditional

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