Set Theory Help

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Anonymous
Set Theory Help 2016-05-05 05:57:37Post No. 114750
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Set Theory Help Anonymous 2016-05-05 05:57:37 Post No. 114750 [Report]

How can I prove Sb5 and Sb6 with the given axioms (Com, As, Dis, Id, Cmp) and the previous Sb's?

For Sb5 I understand I need to use Id, but I don't know where to start. Same with Sb6.

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Anonymous 2016-05-05 07:26:41 Post No.114789
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Anonymous 2016-05-05 07:26:41 Post No.114789 [Report]

>>114750
A∩Ac = Ac∩A = 0 (com, cmp)
A∪Ac = Ac∪A = U (com, cmp)
A'=Ac, B'=A then A=B'=A'c=Acc (sb5)

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Anonymous 2016-05-05 13:03:39 Post No.114905
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Anonymous 2016-05-05 13:03:39 Post No.114905 [Report]

>>114789
Thanks!

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Anonymous 2016-05-06 02:47:20 Post No.115275
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Anonymous 2016-05-06 02:47:20 Post No.115275 [Report]

Bumping this.

I'm still trying to work out Sb5 and I'm getting nowhere.

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Anonymous 2016-05-06 10:44:16 Post No.115379
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Anonymous 2016-05-06 10:44:16 Post No.115379 [Report]

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>>115275
Finally came up with this.

Can anyone check if it's solid? Sub = substitution, H1 = hypothesis 1, H2 = hypothesis 2

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Anonymous 2016-05-06 22:05:39 Post No.115758
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Anonymous 2016-05-06 22:05:39 Post No.115758 [Report]

>>115379
Seems okay, but you can shorten some steps.
Start with (Id) B ∩ U = B
Also in 7-> 8 you need an extra step.