Logic Test - i don't get it

Chronictank · 28 Sep 2011 at 18:28

Could someone please explain to me why the following is Incorrect

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.

I concluded the following venn diagram

Uploaded with ImageShack.us
Grey = impossible

So surely some tracks are routes of transport as it doesn't say that all transport routes are streets?

Chronictank · 28 Sep 2011 at 18:47

nop no extra info.
you basically get the 2 statements a and b, with a concluding statement which you need to decide is correct or incorrect

Another example, this is the question as written in its entirety:

2. a. All Canadians are right handed.
b. All right handed are opticians.

Conclusion is: Some opticians are Canadian.

Is this
Correct
Incorrect

Where the answer is 'correct' as a canadian can be right handed and an optician

Apologies for the badly phrased initial question here it is better formatted

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.

The right answer is that the conclusion is incorrect

Chronictank · 28 Sep 2011 at 18:57

semi-pro waster said:
In that case the answer is that it is incorrect or more accurately the information supplied is still incomplete so you can't actually say whether it is correct or not i.e. defaults to incorrect. Personally I'd be having words with the people who made the test, it really needs an option for "can't say" or similar.

I have been doing this all afternoon, honestly my head is hurting ><
It's for a pilot entry exam so i am afraid it is what it is

Chronictank · 28 Sep 2011 at 18:58

TheCenturion said:
For both, the answer is that the conclusions are incorrect.

The optician one is definitely correct, diagram i made for that one

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All canadians are right handed, so this excludes all the left handed canadians from the scenario
All right handed are opticians, so this excludes all non-opticians from the scenario

Meaning a optician can be either a right handed canadian, or a right handed non-canadian

Chronictank · 28 Sep 2011 at 19:05

At the moment i am cheating and doing the pictures to get the process right in my head, in the exam itself you sit in front of a computer and have to work it all out in your head ><

The next section is a bit better though, it gives you 4 statements and you have to say which the 'most true' is

Chronictank · 28 Sep 2011 at 19:09

I think i am going to go with semi-pro's methodology and assume it is incorrect unless the question mentions it.

Thanks all

Chronictank · 28 Sep 2011 at 19:14

ghost101 said:
Who draws venn diagrams like that?

the guide i found when i was trying to work out why the answer was right lol, the little pictures they did seem to make sense so i just copied to get a mental picture

Chronictank · 28 Sep 2011 at 19:23

Nanoman said:
Yea I'd say they were both incorrect tbh. The first is only stating 'some' when it's all.

The second is just wrong.

it's not 'all' because right handed non-canadians can be an optician too

Chronictank · 28 Sep 2011 at 19:39

aw man now i am even more confused, i think its time for a break :/

Chronictank · 29 Sep 2011 at 00:53

I am really not any the wiser to be entirely honest with you
ok forgetting all the context breaking examples into x,y and z
could you please see if you could spot where i am going wrong

2.
a. All of x are y
b. All of y are z
conclusion: Some z are x

Answer: True

The diagram i get

Uploaded with ImageShack.us

So because Z is the outer shell all of x are z but only some of z can be x

7.
a. None of x is y
b. All of z are y
Conclusion: Some of y are z

Answer: False

My diagram

Uploaded with ImageShack.us
Surely the same is true in this case? all of z are y but only some of y can be z as its the outer shell?

8.
a. None of x is y
b. all of z are x
Conclusion: Some of y are not z

Answer is correct

My diagram

Surely this is incorrect because all of z are not y?

Sorry if i am going in circles i don't get it :confused:

Uploaded with ImageShack.us

All examples from:
http://www.fibonicci.com/logical-reasoning/syllogisms-test/easy/

Chronictank · 29 Sep 2011 at 01:32

Al Vallario said:
The conclusion is false. A racing track is, by definition, a route of transportation. How on earth could some racing tracks not be routes of transportation? It's patently false.

You cannot possibly reach such a false conclusion as the one provided without a false premise. Yet both of the premies are also true.

Hence, the argument is logically invalid.

That's logic.

If you break down the scenario and explain in terms of x, y and z (removing the context) which is essentially what this test is proving

We can say this because a later question is

7. a. None of the A’s is a B.
b. None of the B’s are C.

Conclusion is: All A’s are C’s.

I think this discussion may move somewhere

Chronictank · 29 Sep 2011 at 12:52

My post seems to have been lost in the woodwork so reposting

Chronictank said:
I am really not any the wiser to be entirely honest with you
ok forgetting all the context breaking examples into x,y and z
could you please see if you could spot where i am going wrong

2.
a. All of x are y
b. All of y are z
conclusion: Some z are x

Answer: True

The diagram i get

Uploaded with ImageShack.us

So because Z is the outer shell all of x are z but some of z can be x (because we can't say either way with the information given)

7.
a. None of x is y
b. All of z are y
Conclusion: Some of y are z

Answer: False

My diagram

Uploaded with ImageShack.us
Surely the same is true in this case? all of z are y but some of y can be z as its the outer shell?
(based on the previous example)

8.
a. None of x is y
b. all of z are x
Conclusion: Some of y are not z

Answer is correct

My diagram

Surely this is incorrect because all of z are not y?

Sorry if i am going in circles i don't get it
Uploaded with ImageShack.us

All examples from:
http://www.fibonicci.com/logical-reasoning/syllogisms-test/easy/

Chronictank · 29 Sep 2011 at 14:26

Original questions:
2. a. All Canadians are right handed.
b. All right handed are opticians.

Conclusion is: Some opticians are Canadian.

Canadians = x
Right handed = y
Opticians = z

so
a. All of x are y
b. All of y are z
conclusion: Some z are x
---------------------------------------------
7. a. None of the chemists is an athlete.
b. All managers are athletes.

conclusion is: Some athletes are managers

Chemists = x
Athlete = y
Manager = z

so
a. None of x is y
b. All of z are y
Conclusion: Some of y are z
---------------------------------------------
8. a. None of the bee keepers is a cook.
b. All Dutch are bee keepers.

Conclusion is: Some cooks are not Dutch.

Bee keepers = x
Cook = y
Dutch = z

so
a. None of x is y
b. all of z are x
Conclusion: Some of y are not z