Logic Test - i don't get it

[Nanoman]

And this is a correct diagram for the other question...

So the conclusion 'some opticians are Canadian' is correct.

But in this scenario, all Canadians are opticians. If only some were then that would mean some weren't. Some can't be because ALL Canadians are right handed, and all right handed are opticians.

 

[Kenai]

Indeed. If we replace the names the answer should be the same:

a. All streets are routes of transportation.
b. None of the streets is a racing track.

Conclusion is: Some racing tracks are not routes of transportation.

Answer: Incorrect.

Becomes:

a. All X are Y.
b. None of the X is a Z.

Conclusion is: Some Z are not Y.

Answer: Incorrect.

With the information provided provided we know that all are X are Y but only that some Y are X. We also know that no X is a Z.

We don't have enough information to determine whether some Z are not Y so the conclusion is incorrect.

Exactly this, which is why you shouldn't try and interpret these logic questions based on 'real life truisms', they do nothing other than distract you from the objective of the exercise in the first place.

 

[Frenzy]

The way I was looking at it after thinking about it in a logical way was maybe they are testing your ability to make quick decisions? That's why not all the information is give.

Also I didnt know you could draw venn diagrams as circles within in circiles (shows how much I know ><)

 

[Liampope]

But in this scenario, all Canadians are opticians.

Exactly right - that follows from the two statements a and b. All Canadians are opticians.

If only some were then that would mean some weren't. Some can't be because ALL Canadians are right handed, and all right handed are opticians.

Umm, not sure what you're saying. There's no possibility for only some Canadians being opticians - because the all are - see above.

 

[Al Vallario]

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[Turambar]

On the contrary, there is value in doing so in cases such as these that are based on real life.

If the conclusion of such an argument is that the sky is green and grass is blue, that should give you a hint that something is amiss with the logic.

In this case the conclusion — that some racing tracks are not routes of transportation — is equivalent to the claim the sky is green and grass is blue. Of course all racing tracks are routes of transportation! Hence, we know the conclusion to be false, and we can go about deconstructing the argument from there

That isn't how these tests are constructed though. The premise is often complete nonsense.

 

[Nanoman]

Exactly right - that follows from the two statements a and b. All Canadians are opticians.



Umm, not sure what you're saying. There's no possibility for only some Canadians being opticians - because the all are - see above.

Yea that's what I meant by that statement. Which is why the answer cannot be correct (imo).

 

[BunnyKillBot]

Indeed. If we replace the names the answer should be the same:

a. All streets are routes of transportation.
b. None of the streets is a racing track.

Conclusion is: Some racing tracks are not routes of transportation.

Answer: Incorrect.

Becomes:

a. All X are Y.
b. None of the X is a Z.

Conclusion is: Some Z are not Y.

Answer: Incorrect.

With the information provided provided we know that all are X are Y but only that some Y are X. We also know that no X is a Z.

We don't have enough information to determine whether some Z are not Y so the conclusion is incorrect.

However, none of the Y is a Z giving the conclusion some Z are not Y is still valid. Even though all Z are not Y, it is still valid to say that some Z are not Y, because we have not said anything invalid. Some is a subset of all and therefore still valid.

The conclusion is, imo, correct for this reason.

 

[Liampope]

Also I didnt know you could draw venn diagrams as circles within in circiles (shows how much I know ><)

I don't know if you can or not either! I can't even remember doing venn diagrams it would have been so long ago. My circle within circle within circle diagram was just constructed logically from the two statements - it may break rules for classical Venn diagrams if there are any! But a quick goole image search suggests it's OK.

 

[Liampope]

Yea that's what I meant by that statement. Which is why the answer cannot be correct (imo).

Read carefully - the conclusion was 'some opticians are Canadian', which is correct, not 'some Canadians are opticians', which would be incorrect.

 

[Kenai]

On the contrary, there is value in doing so in cases such as these that are based on real life.

If the conclusion of such an argument is that the sky is green and grass is blue, that should give you a hint that something is amiss with the logic.

In this case the conclusion — that some racing tracks are not routes of transportation — is equivalent to the claim the sky is green and grass is blue. Of course all racing tracks are routes of transportation! Hence, we know the conclusion to be false, and we can go about deconstructing the argument from there

The trouble is, the 'real world' elements are only there so that the test isn't reading X Y and Z as de-constructed above. The point is to test someone's ability to accurately assess (and/or solve) a logical problem when presented with certain information, not for them to embellish the problem with extra assumptions to generate an answer they deem more correct in a real world situation.

In many circumstances the answers will be very much sky=green, in order to see if people are truly solving the logic presented to them rather than making assumptions based on preconceptions.

In the real world, your approach has obvious merit - in the circumstance of a logic test as presented in the OP, it will merely lead you astray from the logical query being posed.

 

[TheCenturion]

Read carefully - the conclusion was 'some opticians are Canadian', which is correct, not 'some Canadians are opticians', which would be incorrect.

Technically the answer is 'can't tell' as it doesn't give information about right handed people who aren't canadian

 

[Liampope]

...it's plainly obvious all racing tracks are routes of transportation

Still disagree . Not sure what your definition of transportation is, but mine would be moving things/people from one place to another. That is not the purpose of a race track - the purpose of a race track is to go round and round in circles for fun. So a race track is not a route of transportation.

 

[Liampope]

Technically the answer is 'can't tell' as it doesn't give information about right handed people who aren't canadian

Eh? It's still perfectly correct to conclude 'some opticians are Canadian'. What non-canadian right-handers may be is irrelevant.

 

[TheCenturion]

Eh? It's still perfectly correct to conclude 'some opticians are Canadian'. What non-canadian right-handers may be is irrelevant.

It's not correct to conclude that, as it is possible that not 'some' but actually 'all' Canadians are opticians. If there was another premise that specifically indicated that there are right handed people who aren't canadian, then the conlusion would be correct. But as it stands, it's not possible to tell whether some opticians are Canadians, or if all of them are.

 

[Al Vallario]

..

 

[Kenai]

Technically the answer is 'can't tell' as it doesn't give information about right handed people who aren't canadian

No, because regardless of whether other right handed people are or aren't we know that SOME opticians are Canadian.

Whether all of them are or only 1% are, is irrelevant, the statement that some are holds true.

 

[Nanoman]

But if all Canadians are right handed and all right handed are opticians. Then all Canadians are opticians or all opticians are Canadian, it doesn't matter which way round it is. The conclusion must therefore be incorrect, as ALL are and not just some, as some would mean that some aren't.

 

[Kenai]

You have a point, but you're misapplying it here.

An argument in which all the premises are realistic (in this case it is broadly correct that all streets are routes of transportation and no streets are racing tracks) but the conclusion is not has a good likelihood of being flawed.

It's a good rule of thumb that is useful in this case, as it is in many others.

Not when the situation is to identify whether two logical clauses denote a conclusion being correct or incorrect, realism has zero relevance.

It is a test to assess the ability to process logical problems, not a test to judge how realistic you deem an answer to be.

 

[TheCenturion]

No, because regardless of whether other right handed people are or aren't we know that SOME opticians are Canadian.

Whether all of them are or only 1% are, is irrelevant, the statement that some are holds true.

I see what you're saying. BUT the problem with questions like this is that you need to define the key words.

If the conclusion has the word 'some' in it, does that then autmatically also mean 'not all'? Because depending on that definition, the answer would change.