Discussion
If the critic's statements are true, which of the following can be concluded?
*This question is included in Exercise Set 3: Intro to Only If / If And Only If, question #10
| (A) | Fred and Barney stop their cars by sticking their feet in very soft dirt, so their feet are not damaged. |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 01/02/2012 13:52
The one instance that would prove the show realistic would be if F and B were disabled. Thus, If F and B are disabled the show is realistic. This is my logic, please explain where I am mistaken.
Posted: 01/05/2012 01:00
Shane,
We've got an "only if" statement here, so let's do a little diagramming:
P 1: The Flintstones TV show would be realistic only if Fred and Barney were both be disabled
P 1: F Real → F/B Dis
P 2: Yet in every scene, both Fred and Barney do have feet.
P 2: ~(F/B Dis)
So if we take the CPos of Premise 1, we get: ~(F/B Dis) → ~(F Real).
And if we look at premise 2, you can see we have ~(F/B Dis).
Therefore, by the CPos of Premise 1, we have ~(F Real).
We've got an "only if" statement here, so let's do a little diagramming:
P 1: The Flintstones TV show would be realistic only if Fred and Barney were both be disabled
P 1: F Real → F/B Dis
P 2: Yet in every scene, both Fred and Barney do have feet.
P 2: ~(F/B Dis)
So if we take the CPos of Premise 1, we get: ~(F/B Dis) → ~(F Real).
And if we look at premise 2, you can see we have ~(F/B Dis).
Therefore, by the CPos of Premise 1, we have ~(F Real).
Posted: 01/05/2012 12:17
Ah, fantastic response! So the: if disabled then realistic solution is correct, but bc we are to assume they are not in fact disabled we cannot assume that answer plausible right? I mean, you said if disabled--> realistic, so the answer is technically true in itself. We just can't give any integrity to the word if bc we know they are not disabled?
Posted: 01/05/2012 22:12
Shane,
I think you've got the right idea, but let's make it clear in case anybody else has questions about this.
Let's say we've got the following statement:
"If we have X, then we must also have Y."
This can be diagrammed: "X → Y"
This means that whenever we have X, we MUST also have Y.
Think of it like this: X will always CAUSE Y to occur.
Now, what if we also have the statement:
"We know for certain we don't have Y."
This can be diagrammed: "~Y"
So what can we conclude given "X → Y" -and- "~Y"?
Well, we can infer that we must NOT have X, because X ALWAYS causes Y, and we know we don't have Y.
What about this scenario: "X → Y" -and- "~X"
What can we infer here? The answer is absolutely nuthin'. It is possible that we have Y, and it is possible that we do NOT have Y. We can't draw any conclusion about Y.
NOTE 1:
You can ALWAYS derive the "contrapositive" relationship from a conditional statement.
So if we have "X → Y", we also know we have "~Y → ~X."
NOTE 2:
You can NEVER simply "flip" a conditional around.
So just because we have "X → Y" does NOT mean we have "Y → X."
NOTE 3:
You can NEVER simply negate the terms of a conditional without reversing the order.
So just because we have "X → Y" does NOT mean we have "~X → ~Y."
I think you've got the right idea, but let's make it clear in case anybody else has questions about this.
Let's say we've got the following statement:
"If we have X, then we must also have Y."
This can be diagrammed: "X → Y"
This means that whenever we have X, we MUST also have Y.
Think of it like this: X will always CAUSE Y to occur.
Now, what if we also have the statement:
"We know for certain we don't have Y."
This can be diagrammed: "~Y"
So what can we conclude given "X → Y" -and- "~Y"?
Well, we can infer that we must NOT have X, because X ALWAYS causes Y, and we know we don't have Y.
What about this scenario: "X → Y" -and- "~X"
What can we infer here? The answer is absolutely nuthin'. It is possible that we have Y, and it is possible that we do NOT have Y. We can't draw any conclusion about Y.
NOTE 1:
You can ALWAYS derive the "contrapositive" relationship from a conditional statement.
So if we have "X → Y", we also know we have "~Y → ~X."
NOTE 2:
You can NEVER simply "flip" a conditional around.
So just because we have "X → Y" does NOT mean we have "Y → X."
NOTE 3:
You can NEVER simply negate the terms of a conditional without reversing the order.
So just because we have "X → Y" does NOT mean we have "~X → ~Y."
Posted: 03/07/2012 22:19
I don't understand how "C" would not be correct. It states "the Flinstones would be realistic only if Fred and Barney were both disabled". "c" states "the Flinstones would be realistic if Fred and Barney were both disabled". That's exactly what the question states the only thing that would make the Flinstones realistic, so I fail to see how that answer is wrong.
Posted: 03/17/2012 13:49
I hate the stupid X and Y and arrows garbage too...I'll explain this better...
So it says that the show can be real ONLY IF they're disabled, so basically it's saying that if the show is real, then they're disabled; however, it still leaves us the possibility that they are disabled and the show isn't real
So it says that the show can be real ONLY IF they're disabled, so basically it's saying that if the show is real, then they're disabled; however, it still leaves us the possibility that they are disabled and the show isn't real
[X only if Y] means: X implies Y, because the ONLY way that X can happen is if Y has happened; therefore if X happens, Y happened
[X if Y] means: Y implies X,
because IF Y happens then X will happen
Well I hope you understand, but I might as well give you another explanation while I'm at it:
[If X, then Y] means: X implies Y,
because if X happens, then Y will happen
If you still fail to understand, just retread what I've said, and take careful notice at the tenses of the words [especially happen(s)(ed)].