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On August 19 2008 11:05 AcrossFiveJulys wrote:Show nested quote +On August 19 2008 10:02 Mindcrime wrote: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.
The reverse of "4 is false, 5 is true" is "4 is true, 5 is false."
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the real answer
+ Show Spoiler + assume 5 is true. 5 says 1 is true and 3 are true. ok so look at 1. 1 says 3 is false. direct contradiction with 5 saying that 3 is true.
so 5 IS FALSE. and we can rule out anything else that says 5 is true.
therefore 3 IS FALSE because it claims so. and by chain combo logic, anything saying 3 is true is also false.
so 2 IS FALSE for claiming so. the only thing that can be true is either 1 or 4. and because 4 says 2 is true, which we just prove is totally bogus, 4 is also bogus by the bogus-transitive property.
1 IS TRUE.
Check: 1 says 2 and 3 are false.
2 claims than 1 is false and 3 is true. that is not consistnet with 1. checks out
3 claims that 4 is false and 5 is true. 5 is not true, so that is also not consistent with 1. checks out.
1 IS TRUE
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On August 19 2008 11:28 Mindcrime wrote:Show nested quote +On August 19 2008 11:05 AcrossFiveJulys wrote:On August 19 2008 10:02 Mindcrime wrote: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. The reverse of "4 is false, 5 is true" is "4 is true, 5 is false."
Please read some basic logic theory.
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On August 19 2008 06:57 Mindcrime wrote:
Does "false" mean "completely false"?
no false means the entire the is not true.
if i say "bush is a jackass, cheyney is the devil, and bill clinton did not screw monica lewinsky", then we can say about the statement as a whole "it is false", because we know bill clinton did screw monica lewinsky.
now if only bills were rejected as a whole for having one inkling taint. christmas trees would die forever.
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On August 19 2008 12:04 AcrossFiveJulys wrote:Show nested quote +On August 19 2008 11:28 Mindcrime wrote:On August 19 2008 11:05 AcrossFiveJulys wrote:On August 19 2008 10:02 Mindcrime wrote: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. The reverse of "4 is false, 5 is true" is "4 is true, 5 is false." Please read some basic logic theory.
The OP says "reverse".
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On August 19 2008 12:13 Mindcrime wrote:Show nested quote +On August 19 2008 12:04 AcrossFiveJulys wrote:On August 19 2008 11:28 Mindcrime wrote:On August 19 2008 11:05 AcrossFiveJulys wrote:On August 19 2008 10:02 Mindcrime wrote: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. The reverse of "4 is false, 5 is true" is "4 is true, 5 is false." Please read some basic logic theory. The OP says "reverse".
then the op is wrong and doesn't understand logic, because if that's true it means the process by which I reached my conclusion (which was logically valid, even if you take that "reverse" rule into account) would be wrong and the system in which the problem is based is flawed.
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+ Show Spoiler +FTFTF
run the statement from 1 to 5 once.
just to add, bad wording!!
please use the word 'and', or ppl going to assume false meaning either, 'OR' is not true.
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read through it once, i don't want to think about it because i just got back from band camp which is fucking tiring as hell.
3+5true
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On August 19 2008 12:18 AcrossFiveJulys wrote:Show nested quote +On August 19 2008 12:13 Mindcrime wrote:On August 19 2008 12:04 AcrossFiveJulys wrote:On August 19 2008 11:28 Mindcrime wrote:On August 19 2008 11:05 AcrossFiveJulys wrote:On August 19 2008 10:02 Mindcrime wrote: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. The reverse of "4 is false, 5 is true" is "4 is true, 5 is false." Please read some basic logic theory. The OP says "reverse". then the op is wrong and doesn't understand logic, because if that's true it means the process by which I reached my conclusion (which was logically valid, even if you take that "reverse" rule into account) would be wrong and the system in which the problem is based is flawed. Oh for heaven's sake, just accept that you read the OP too quickly and didn't notice one of the rules. The problem is entitled to define its terms however it likes--if it defines "false" as "the reverse is true", then that's what "false" means in the context of the problem. It has nothing to do with "understanding logic".
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Lots of disagreement. I'll give it a try:
+ Show Spoiler +
Givens:
1 ⇔ ¬2 ∧ ¬3
2 ⇔ ¬1 ∧ 3
3 ⇔ ¬4 ∧ 5
4 ⇔ 2 ∧ ¬3
5 ⇔ 1 ∧ 3
Let's test statement 1, by assuming 1 is true.
A. 1 ⇔ ¬2 ∧ ¬3; let's test the individual components ¬2 and ¬3
B. ¬2 ⇔ ¬(¬1 ∧ 3) ⇔ 1 ∨ ¬3
We are assuming 1 is true, so that holds. How about ¬3? (Note that we are still interested in ¬3 because of statement A, not statement B)
C. ¬3 ⇔¬(¬4 ∧ 5) ⇔ 4 ∨ ¬5
Let's test 4 and ¬5, then.
D. 4 ⇔ 2 ∧ ¬3
But we already have ¬2. So let's check the other term from C, ¬5
E. ¬5 ⇔ ¬(1 ∧ 3) ⇔ ¬1 ∨ ¬3
¬3 we already hold to be true, so E is satisfied, which satisfies C, and so on... so statement 1 is possibly TRUE.
So far, if we assume that 1 is true, we find a consistent result that:
1, ¬2, ¬3, ¬4, ¬5.
Bleh, too lazy to go through all the statements -_- someone else can give it a try
Hah, I guess I was lucky in choosing to start with 1.
AcrossFiveJulys's logic is correct. If you negate "A AND B," then you'll end up with "!A OR !B," not "!A AND !B."
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On August 19 2008 12:40 qrs wrote:Show nested quote +On August 19 2008 12:18 AcrossFiveJulys wrote:On August 19 2008 12:13 Mindcrime wrote:On August 19 2008 12:04 AcrossFiveJulys wrote:On August 19 2008 11:28 Mindcrime wrote:On August 19 2008 11:05 AcrossFiveJulys wrote:On August 19 2008 10:02 Mindcrime wrote: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. The reverse of "4 is false, 5 is true" is "4 is true, 5 is false." Please read some basic logic theory. The OP says "reverse". then the op is wrong and doesn't understand logic, because if that's true it means the process by which I reached my conclusion (which was logically valid, even if you take that "reverse" rule into account) would be wrong and the system in which the problem is based is flawed. Oh for heaven's sake, just accept that you read the OP too quickly and didn't notice one of the rules. The problem is entitled to define its terms however it likes--if it defines "false" as "the reverse is true", then that's what "false" means in the context of the problem. It has nothing to do with "understanding logic".
yeah but if you reverse it like it says to in the op there is no answer, you just get contradictions.. This implies to me the op forgot the details of the question and made a mistake in the instructions.
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"Reversing" a statement has no logical meaning. There is negation, there is taking the inverse, there is taking the converse.... there is no "reverse" of a statement.
The negation, or the "NOT A" of a statement A, is probably the correct interpretation and yields a consistent result.
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Canada7170 Posts
+ Show Spoiler +
Assume 5 is true.
3 and 1 are then true. But 1 says 3 is false.
So 5 must be false.
3 is then false.
so 2 is then false.
Then 4 is false.
1 is true.
TFFFF
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mikeymoo, you can't justify "5 is false, therefore 3 is false." It could be 1 that is false, and 3 could be true at that point.
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no solution..
two statement saying eachother is T both has to have the same real value (ie. both true or both false), two statement saying eachother is false both has to have different value.
On August 19 2008 13:16 sYz-Adrenaline wrote:
F F T F T
so 5 is true, and 5 says that 1 is true, but 1 is false?? lol there is no solution dude.
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AcrossFiveJulys said everithing that should be said in this case...
please... study some logic...
!(P AND Q)= !P OR !Q
+ Show Spoiler +
1 true, everithing else is false, just need to find a contradiction, and with 5 is easy to find, but try and u will find it on 2,3 and 4 too
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Glider.... 1 true and the rest false is consistent. I don't think any other scenario is consistent, as proven by AcrossFiveJulys. "No solution" is the wrong answer.
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On August 19 2008 14:49 BottleAbuser wrote:
Glider.... 1 true and the rest false is consistent. I don't think any other scenario is consistent, as proven by AcrossFiveJulys. "No solution" is the wrong answer.
that is only right if 1 false perimeter makes the whole statement false... which i guess makes sense but if you read the condition at the beginning..
On August 19 2008 06:29 X.xDeMoNiCx.X wrote:
each true keeps the statement the same, each false reverses it.
in this case a false statement 5 would mean that statement 1 is false also...
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EPT
