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On August 19 2008 07:54 Neverborn wrote:
Okay. I'll start with the ones that cannot be true:
2 and 3 cannot be true. If they were true, then three would also be true. Three says that five is true, which says that three is false. Since they can't agree, they are both out.
4 cannot be true because it says that 2 is true.
1 says that 2 and 3 are false, 5 says that 1 is true and 3 is false. Those two are in agreement, and since 2 and 3 are certifiably false, we know that they are true as well.
1,5 True
2-4 False
/thread
Nope, 5 says 3 is true.
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On August 19 2008 08:14 qrs wrote:
edit: decided not to be snarky. Neverborn, your mistake is in assuming that not-true is the same as false here.
No, his mistake was misreading #5. :p
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eh, maybe i was wrong o.O, i could of swore it said 1 was true and 3 was false x.x
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Has this been solved yet?
+ Show Spoiler +
statement 1) 2 and 3 are false.
statement 2) 1 is false, 3 is true.
statement 3) 4 is false, 5 is true.
statement 4) 2 is true, 3 is false.
statement 5) 1 is true, 3 is true.
Assume 1 is true:
2 is false -> 1 is true, 3 is false
3 is false -> 4 is true, 5 is false
4 is true -> 2 is true
RAA: 1 is false
When 1 is false, 5 is false.
When 5 is false, 3 is false.
Therefore making 4 and 2 true.
However, 2 says that 3 is true
So there is no answer.
Unless you take the path that "not false" doesn't mean "true." Then you only look at the "true" values:
Assume 2 is true:
3 is true
5 is true
1 is true, which contradicts 2 being true
Assume 3 is true:
5 is true
1 is true
can work.
Assume 4 is true:
2 is true
3 is true
5 is true
1 is true, contradicting 2 being true
Assume 5 is true:
1 is true
3 is true
5 is true
Assume 1 is true:
nothing.
Therefore, 1, 3, 5.
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5 is false because there is a conflict of logic if it's not. Following that:
My logic:
5F -> 1F, 3F
3F -> 4T, 5F
4T -> 2T, 3F
2T -> 1F, 3T
1F -> 2T, 3F
which works as far as I know since statement one states that 2 and 3 are false. The 'and' is misleading since statement 1 is false if statement 2 _or_ 3 is true. No assumptions required.
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+ Show Spoiler +Assume statement 1 is true, and the rest are false.
Statement 1 is valid because we're assuming both 2 and 3 are false.
Statement 2 is false because 1 is true, and says 2 is false
Statement 3 is false because 1 is true, and says 3 is false.
Statement 4 is false because it says 2 is true, but 2 is actually false.
Statement 5 is false because it says 3 is true, but 3 is actually false.
Yeah, it's all based on assumptions, but based on that assumption, everything checks out.
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was bored, came back to check
LOL at my answer
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On August 19 2008 09:07 Jin wrote:
5 is false because there is a conflict of logic if it's not. Following that:
My logic:
5F -> 1F, 3F
3F -> 4T, 5F
4T -> 2T, 3F
2T -> 1F, 3T
1F -> 2T, 3F
which works as far as I know since statement one states that 2 and 3 are false. The 'and' is misleading since statement 1 is false if statement 2 _or_ 3 is true. No assumptions required.
If 2 is true then 3 is true then 5 is true. :|
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On August 19 2008 09:17 Mindcrime wrote:Show nested quote +On August 19 2008 09:07 Jin wrote:
5 is false because there is a conflict of logic if it's not. Following that:
My logic:
5F -> 1F, 3F
3F -> 4T, 5F
4T -> 2T, 3F
2T -> 1F, 3T
1F -> 2T, 3F
which works as far as I know since statement one states that 2 and 3 are false. The 'and' is misleading since statement 1 is false if statement 2 _or_ 3 is true. No assumptions required. If 2 is true then 3 is true then 5 is true. :|
Oops you are right
K, starting with 5T then:
5T -> 1T, 3T
3T -> 4F, 5T
4F -> 2F, 3T
2F -> 1T, 3F
which is another conflict
I;m confused
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You fail again. 
EDIT: I posted before your edit~
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all F
edit: unless the false here does not imply logical not, which I'm assuming it does
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On August 19 2008 08:39 Yank31 wrote:Show nested quote +On August 19 2008 08:14 qrs wrote:
edit: decided not to be snarky. Neverborn, your mistake is in assuming that not-true is the same as false here. well... Show nested quote +On August 19 2008 06:29 X.xDeMoNiCx.X wrote:
...
each true keeps the statement the same, each false reverses it.
...
Right. If a multiple-part statement is not true, it doesn't follow that its reverse is necessarily true.
But anywayOn August 19 2008 08:52 SonuvBob wrote:Show nested quote +On August 19 2008 08:14 qrs wrote:
edit: decided not to be snarky. Neverborn, your mistake is in assuming that not-true is the same as false here. No, his mistake was misreading #5. :p my bad: didn't reread the OP. Even if neverborn had been right about #5, his answer would still be wrong, for the reason I mentioned.
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one answer:
+ Show Spoiler +
Proof that 5 is false by contradiction:
1) Assume 5 is true. This implies that 1 is true and 3 is true.
2) Since 1 is true, both 2 and 3 are false. But this is a contradiction; 5 said 3 is true. Thus, 5 must be false.
Now we know 5 is false. Let's find any statements that say 5 is true. Statement 3 says 5 is true. Thus, statement 3 must be false.
Now let's find statements which say 3 is true. Both 2 and 5 say 3 is true; thus, both 2 and 5 must be false (we already knew 5 was false).
Finally, we find any statements that say 2 is true. Statement 4 says 2 is true, thus 4 must be false.
So far, we have proved that 2,3,4, and 5 are all false. Let's look at statement 1. Statement 1 says both statements 2 and 3 are false. Hence, statement 1 must be true.
Hence, we have figured out the values of all five statements:
1 is true, and 2,3,4,5 are all false.
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Oh god sounds like a UMAT question ><
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On August 19 2008 09:37 AcrossFiveJulys wrote:one answer: + Show Spoiler +
Proof that 5 is false by contradiction:
1) Assume 5 is true. This implies that 1 is true and 3 is true.
2) Since 1 is true, both 2 and 3 are false. But this is a contradiction; 5 said 3 is true. Thus, 5 must be false.
Now we know 5 is false. Let's find any statements that say 5 is true. Statement 3 says 5 is true. Thus, statement 3 must be false.
Now let's find statements which say 3 is true. Both 2 and 5 say 3 is true; thus, both 2 and 5 must be false (we already knew 5 was false).
Finally, we find any statements that say 2 is true. Statement 4 says 2 is true, thus 4 must be false.
So far, we have proved that 2,3,4, and 5 are all false. Let's look at statement 1. Statement 1 says both statements 2 and 3 are false. Hence, statement 1 must be true.
Hence, we have figured out the values of all five statements:
1 is true, and 2,3,4,5 are all false.
If 1 is true then 3 is false then 5 is false then 1 is false.
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+ Show Spoiler +
Order of Operation:
statement 1) 2 and 3 are false. 1T2F3F4T5T
statement 2) 1 is false, 3 is true. 1T2F3F4T5T (Works good so far)
statement 3) 4 is false, 5 is true. 1T2F3F4T5F (Good)
statement 4) 2 is true, 3 is false. 1T2T3F4T5F (Everythings Fine)
statement 5) 1 is true, 3 is true. 1F2T3F4T5F (A bit of switching)
1F2T3T4T5F (Starting from beginning again)
1F2T3T4T5F (After 2)
1F2T3T4F5T (After 3)
I quit, dinner time
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+ Show Spoiler +
statement 1) 2 and 3 are false.
statement 2) 1 is false, 3 is true.
statement 3) 4 is false, 5 is true.
statement 4) 2 is true, 3 is false.
statement 5) 1 is true, 3 is true.
statement 1) = OK
statement 2) = OK
statement 3) = OK
statement 4) = 3 reverses to <b>true</b>! 2 stays the same <b>false</b>
statement 5) = 3 stays the same and so does 1.
1 F
2 F
3 T
4 F
5 T
Ez 
Check PLz ?
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On August 19 2008 10:02 Mindcrime wrote:Show nested quote +On August 19 2008 09:37 AcrossFiveJulys wrote:one answer: + Show Spoiler +
Proof that 5 is false by contradiction:
1) Assume 5 is true. This implies that 1 is true and 3 is true.
2) Since 1 is true, both 2 and 3 are false. But this is a contradiction; 5 said 3 is true. Thus, 5 must be false.
Now we know 5 is false. Let's find any statements that say 5 is true. Statement 3 says 5 is true. Thus, statement 3 must be false.
Now let's find statements which say 3 is true. Both 2 and 5 say 3 is true; thus, both 2 and 5 must be false (we already knew 5 was false).
Finally, we find any statements that say 2 is true. Statement 4 says 2 is true, thus 4 must be false.
So far, we have proved that 2,3,4, and 5 are all false. Let's look at statement 1. Statement 1 says both statements 2 and 3 are false. Hence, statement 1 must be true.
Hence, we have figured out the values of all five statements:
1 is true, and 2,3,4,5 are all false.
If 1 is true then 3 is false then 5 is false then 1 is false.
Negative. If 1 is true, then 3 is false, I agree. But, if 3 is false, then it's the opposite of "4 is false and 5 is true", which is equivalent to: "4 is true AND 5 is true, OR 4 is true AND 5 is false, OR 4 is false AND 5 is false."
Edit: for clarity, I'm showing you the first untrue statement you made which means your conclusion isn't valid.
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:edit:mis understood hte perms on how this is done. i'll do it later my first conclusion was all are false because the statement conflict with their own true or false but that is taking statement 5 as a truth.
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EPT
