Logic Test - i don't get it

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.

But the answer would be 'can't tell', because it's possible that there are right handers who are not canadian, but we don't know for sure.
 
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.

The word some is defined very clearly in many dictionaries.

It does not preclude 'all', so the conclusion is correct.
 
The word some is defined very clearly in many dictionaries.

It does not preclude 'all', so the conclusion is correct.

In that case, if the word 'all' can be considered a subset of 'some' then the conclusion would be correct. However, it's badly worded. IT would be better written as 'At least some canadians are opticians'
 
Goodness me. It's a rule of thumb. It is helpful in many cases, this being one of them.

Entirely realistic premises followed by an entirely unrealistic conclusion usually means there's something up with the logic of an argument.

What part of that don't you understand? :confused:

I understand all of it, what you seem to be missing is the point that applying realisms to a test designed to test purely your abilities to resolve logic statements against specified conclusions is irrelevant.

I already said, in a real world situation your approach has merit. In this sort of test it is completely missing the point of the exercise, which is to test your ability to solve logic. Hence the post earlier in the thread about how your answer should not change regardless of what is contained within those statements, it is the logic of the statements you are solving, not the content.

As I said before, in many cases the answer may 'in real terms' seem entirely stupid and this is done purposely to make sure it is the logic you are solving and not the content.
 
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In that case, if the word 'all' can be considered a subset of 'some' then the conclusion would be correct. However, it's badly worded. IT would be better written as 'At least some canadians are opticians'

Merriam-Webster define some as 'being at least one' anyway :p
 
TheCenturion, Nanoman - you're making it much harder than it really is! (unless I'm missing something). Look at my wobbly diagram again - do you dispute it? It follows logically from the statements a and b. From my diagram clearly 'some opticians are Canadian' is a true statement. Non-Canadian right-handers and the definition of some possibly including all dont need to come into it. Can you construct a diagram that satisfies the statements a and b for which the statement 'some opticians are Canadian' is false?
 
Goodness me. It's a rule of thumb. It is helpful in many cases, this being one of them.

Entirely realistic premises followed by an entirely unrealistic conclusion usually means there's something up with the logic of an argument.

What part of that don't you understand? :confused:

Consider this harder multiple choice question from here.

a. All dogs are brown.
b. All pitbulls are brown.


1.Some pitbulls are dogs
2.Some dogs are pitbulls
3.All pitbulls are dogs
4.None of the conclusions above is correct

In the real world we know a pitbull is a dog. In this example we don't.
 
Consider this harder multiple choice question from here.

a. All dogs are brown.
b. All pitbulls are brown.


1.Some pitbulls are dogs
2.Some dogs are pitbulls
3.All pitbulls are dogs
4.None of the conclusions above is correct

In the real world we know a pitbull is a dog. In this example we don't.

Surely here, the answer is number 4?
 
Goodness me. It's a rule of thumb. It is helpful in many cases, this being one of them.

Entirely realistic premises followed by an entirely unrealistic conclusion usually means there's something up with the logic of an argument.

What part of that don't you understand? :confused:

It's a logic test. Logic is an absolute science - you do not apply rules of thumb and real life knowledge or you will make conclusions that you may know to be correct in real life, but aren't strictly speaking logical. As Turambar's example demonstrates perfectly.
 
Surely here, the answer is number 4?

Indeed, when you solve the pure logic presented and not the 'real world truisms' of the examples, which is the point I am trying to get across to Al Vallario - the objective is to solve the logic, not interpret a real world situation and apply 'external knowledge'.

Many such tests even try and trip you up by making the logical answer seem realistically stupid, to make you doubt yourself and thus see if you are solving the logic or interpreting things.
 
Indeed, when you solve the pure logic presented and not the 'real world truisms' of the examples, which is the point I am trying to get across to Al Vallario - the objective is to solve the logic, not interpret a real world situation and apply 'external knowledge'. Many such tests even try and trip you up by making the logical answer seem realistically stupid, to make you doubt yourself and thus see if you are solving the logic or interpreting things.

Yeah. The whole point of these questions is to attempt to verify a conclusion using only premises given. I've seen loads of questions where the answer actually contradicts real world knowledge. I think that's there to confuse people who try to use external knowledge to answer the question.

Also I think we know that not all canadians are right handed :p
 
Just to clarify, this is the correct Venn diagram:

bm6rV.png

This would roughly be my venn diagram as well.

A good trick for these is to ignore what the english words mean, instead simply assign symbols.

Reading "A implies B; B implies C; A is true: therefore C is true" etc. will help stop you putting any irrelevent realworld knoweldge in.
You must think in abtract terms.
 
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TheCenturion, Nanoman - you're making it much harder than it really is! (unless I'm missing something). Look at my wobbly diagram again - do you dispute it? It follows logically from the statements a and b. From my diagram clearly 'some opticians are Canadian' is a true statement. Non-Canadian right-handers and the definition of some possibly including all dont need to come into it. Can you construct a diagram that satisfies the statements a and b for which the statement 'some opticians are Canadian' is false?

You're missing my previous point, Kenai summed it up. My previous definition of some was somewhat out. I had assumed that some only accounted for a certain percentage meaning that the conclusion could state that some opticians were not Canadian. Where as some defined by Webster, denotes an undetermined amount, which means the statement is correct, some are.
 
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This would be my venn diagram as well.

You have no information telling you what the interaction between route of transport and race track is though, you could draw multiple completely valid venn diagrams for that particular problem.

On that basis I would say 'not answerable'
 
You're missing my previous point, Kenai summed it up. My previous definition of some was somewhat out. I had assumed that some only accounted for a certain percentage meaning that the conclusion could conclude that some opticians were not Canadian. Where as some defined by Webster, denotes an undetermined amount, which means the statement is correct, some are.

Sorry I still dont understand you!:) What's the difference between 'a certain percentage' and 'an undetermined amount'? Sounds the same to me. Whichever your definition, the statement 'some opticians are Canadian' is always logically true. Ah well it's late - gotta be up in... oh crap - 4.5 hours :(

EDIT: oh wait you edited! The alternative conclusion 'some opticians are not Canadian' is also true. There was nothing wrong with your definition of some. It just means, well, some!
 
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