Contrapositives: book error or my error? Forum

[speedwagon]

Hello from logic game boot camp, aka hell, but a fun hell. I am stuck on a problem and am unsure if it's me or the book:

I'm working on grouping games, and here's what I have, abstracted somewhat for copyright purposes (If this is still a copyright violation rather than fair use, I will take it down!)

X is the in group.

If X contains T, it contains Q
If X contains D, it does not contain C
If X does not contain T, it contains H
If X contains D or Q, it contains H

So I logic this out (with ! for negation):
If T, Q
If !Q, !T (edited per below comment so folks don't keep stopping here)
If D, !C
If C, !D
IF !T, H
If !H, T
If (D OR Q), H -> If !H, !D AND !Q

which condenses to:
If !H, !D, !Q, T - BUT WAIT. We have a rule, If T, then Q, which means Q both must and must not be involved.

Did I miss something? Or did the book? Thanks a ton.

[lymenheimer]

Your contrapositive is wrong. So:
If T, then Q
Contra: !Q, then !T

[speedwagon]

Thank you. I had been over it 100 times and it figures I missed the one that should've been easiest to spot.

[speedwagon]

You know what, I realize I made a transcription error, but I don't think it changes the problem q:
X is the in group.

If X contains T, it contains Q
If X contains D, it does not contain C
If X does not contain T, it contains H
If X contains D or Q, it contains H

So I logic this out (with ! for negation):
1) If T, Q
2) If !Q, !T <-- fixed it
3) If D, !C
4) If C, !D
5) IF !T, H
6) If !H, T
7) If (D OR Q), H -> If !H, !D AND !Q

which condenses to:
If !H:
!D, !Q, (7)
T (6)
!T (per 7, then 2)

Is there something else wrong here? Thanks a ton.

[lymenheimer]

Thank you. I had been over it 100 times and it figures I missed the one that should've been easiest to spot.

Not sure that completely addresses your question though, but just thought i'd point it out

[foggynotion]

Speedwagon, I don't see any errors in your rundown on the clues. Your symbolization and contrapositives all look good. If the assumption that H is out leads to a contradiction, all that means is that H must be in. There's no mistake there that I can see.