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### #1 superprismatic

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Posted 08 December 2010 - 09:38 PM

Let A, B, C, D, and E be statements. Consider the following
four statements made from these using the usual five sentential
connectives ~, ∨, &, →, and ↔ (explained below):
I: (((A&B)∨(B↔A))∨E)↔(((C↔(C∨<img src='http://brainden.com/forum/public/style_emoticons/<#EMO_DIR#>/cool.gif' class='bbc_emoticon' alt='B))' />&A)∨(E&A))
II: ((~((D∨((A&(D→<img src='http://brainden.com/forum/public/style_emoticons/<#EMO_DIR#>/cool.gif' class='bbc_emoticon' alt='B))' />∨((~C∨A)∨<img src='http://brainden.com/forum/public/style_emoticons/<#EMO_DIR#>/cool.gif' class='bbc_emoticon' alt='B))' />)∨E)∨E)&A)↔A
III: ((~A∨(C→A))&~C)→(B→(B→((((A∨B)&A)∨E)&A)))
IV: (A&(E→((E∨A)→E)))→((((E→A)↔D)↔(E↔C))∨E)
Which of the following statements are derivable from
the above set of four statements, and which are not?
Statement 1: B∨(C∨(E&(D&(E∨((~E→A)&(A∨(E↔(C&<img src='http://brainden.com/forum/public/style_emoticons/<#EMO_DIR#>/cool.gif' class='bbc_emoticon' alt='B))' />))))))
Statement 2: (((((A↔D)↔(B→D))&D)↔(((C∨E)→D)∨<img src='http://brainden.com/forum/public/style_emoticons/<#EMO_DIR#>/cool.gif' class='bbc_emoticon' alt='B))' />∨A)↔B
Statement 3: (~(((C&B)∨A)&C)→A)∨(A&(E→(C∨(E→(B∨C)))))
Statement 4: B∨(E↔(A↔(~(B&((E∨((E∨A)→A))↔<img src='http://brainden.com/forum/public/style_emoticons/<#EMO_DIR#>/cool.gif' class='bbc_emoticon' alt='B))' />∨(A&D))))
Statement 5: A↔(((B↔C)&E)∨((D&B)&(D∨((A&D)&(E↔A)))))
Statement 6: (((((E∨~A)∨C)↔D)→((B↔D)↔D))∨A)&(E↔(E&A))
The five sentential connectives are:
1. ~ (not) ~X is true when X is false and ~X is false when X is true.
2. ∨ (or) X∨Y is true when at least one of X and Y is true, otherwise it is false.
3. & (and) X&Y is true when both X and Y are true; otherwise it is false.
4. → (implication) X→Y is true unless X is true and Y is false, in which case it is false.
5. ↔ (equivalence) X↔Y is true when X and Y have the same truth value, otherwise it is false.

In case someone would rather have the RPN version of the
statements, I include them below:
I: AB&BA↔∨E∨CCB∨↔A&EA&∨↔
III: A~CA→∨C~&BBAB∨A&E∨A&→→→
IV: AEEA∨E→→&EA→D↔EC↔↔E∨→
Statement 1: BCEDEE~A→AECB&↔∨&∨&&∨∨
Statement 3: CB&A∨C&~A→AECEBC∨→∨→&∨
Statement 6: EA~∨C∨D↔BD↔D↔→A∨EEA&↔&

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### #2 araver

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Posted 09 December 2010 - 12:27 AM

I'm just a bit confused, so I guess I need to ask this first:
Spoiler for

Edited by araver, 09 December 2010 - 12:28 AM.

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### #3 superprismatic

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Posted 09 December 2010 - 01:24 AM

I'm just a bit confused, so I guess I need to ask this first:

Spoiler for

Spoiler for well...

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### #4 LReese

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Posted 09 December 2010 - 11:33 PM

Edited by LReese, 09 December 2010 - 11:42 PM.

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### #5 superprismatic

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Posted 10 December 2010 - 04:49 PM

Spoiler for

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### #6 LReese

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Posted 10 December 2010 - 09:09 PM

Spoiler for

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### #7 LReese

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Posted 10 December 2010 - 09:53 PM

How does this work, if you get the answer you post it, of course, but is anything else reqired? Do you get some kind of credit for a correct answer?
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### #8 superprismatic

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Posted 10 December 2010 - 10:04 PM

How does this work, if you get the answer you post it, of course, but is anything else reqired? Do you get some kind of credit for a correct answer?

Spoiler for No credit, you just do it for the fun of it...

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### #9 LReese

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Posted 11 December 2010 - 12:46 AM

Thanks for the info, I've been reading the help file and not finding exactly what i was curious about. First, thanks for the puzzle, it was an enjoyable challenge, although I feel I may have taken the long way to figure it out. Second, if you don't mind answering, how do members advance from a NEWBIE?
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### #10 superprismatic

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Posted 11 December 2010 - 01:18 AM

Thanks for the info, I've been reading the help file and not finding exactly what i was curious about. First, thanks for the puzzle, it was an enjoyable challenge, although I feel I may have taken the long way to figure it out. Second, if you don't mind answering, how do members advance from a NEWBIE?

That rank is purely a reflection of the number of posts. So, it's really is a measure of activity. I wouldn't worry about it if I were you. I've seen NEWBIEs around here who are obviously PhDs in math related topics. I've also seen teenagers who are advanced members. Most of us just love math and logic problems. That's the main thing around these here parts, partner!
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