# Thread: The Logic Test - What do YOU score?

1. 19/26. I was confused as to whether or not to use common knowledge - I know that Ithaca is in NY for example. I found the letter questions easier (and I scored higher) because then the common knowledge issue didn't play into it.

2. 20/26

I took that test a couple months ago and got 15/26 (+ or - 1). I feel like I'm developing, or something.

It's official: I suck at logic.

4. Originally Posted by Lateralus
26/26, this was easy. Just use Venn diagrams!
Yea, you're not supposed to use any calculus first time round

5. 25/26 by eyeballing, no paper or charts... I must say I'm disappointed...

6. Originally Posted by 6sticks
21/26.
Same.

7. Can someone please explain how #5's premises are not inconsistent?

If they are, all of the conclusions follow because the "additional premises" that you need to derive whatever you want are implied by the inconsistent set premises.

So, while the conclusions may not be immediately derivable given the statements, one could use this language's transformation rules to derive additional conclusions that would enable the logician to show that each of the conclusions listed do in fact follow from the premises!

:steam:

8. 1st time: 19/26
2nd time -- without checking answers: 24/26

9. Only 18/26.

10. Originally Posted by Owl
Can someone please explain how #5's premises are not inconsistent?

If they are, all of the conclusions follow because the "additional premises" that you need to derive whatever you want are implied by the inconsistent set premises.

So, while the conclusions may not be immediately derivable given the statements, one could use this language's transformation rules to derive additional conclusions that would enable the logician to show that each of the conclusions listed do in fact follow from the premises!

:steam:
P: (1) Some A that are B are not C that are D
(2) All A are C

C: a. Some A that are D are C that are B
b. Some C are not D
c. Some B are not C
d. Some A are D

NB: Instead of using an ampersand (&) I'll use a hyphen for conjunctive relationships... easier to read...

- Some A are B... (from 1)
- Of those A-B, there are some A-B which are not C-D... (from 1)
To paraphrase this last one... there are A-Bs which are not-also C-Ds... but that doesn't necessarily mean that there aren't A-B's which are C-notD's... again, in other words, of A-Bs which are C's they don't necessarily have to have/be D.
- All A are C (from 2)

For fun and ease of comprehension, let's paraphrase these two premises...

(1) "There exist some females(A) that are human(B) which are not living things(C) with x-ray vision(D)." Or E(x) | A-B -> NOT C-D.
(2) "All females(A) are living things(C)." or A(x) | A -> C

To explain why the premises aren't inconsistent... the only two assertions of existence available for our use are that

- there are A's and all of them are C.... those females which exist are all living things...

- there exist A's that are also B.... which are not also C's which are D.... there exist females that are also human, but which at the same time are not living x-ray vision-endowed beings... that doesn't contradict the statement that all females are living things (All A's are C)... I can truthfully say that I'm not a living thing with x-ray vision... I can also truthfully say that I'm a living thing. This involves the notions that an "AND" statement (C-D) is only true if both propositions involved in the conjunction are true... if one, say C, is true, while the other, say D, is false, the conjunction C-D is false. Hence, I can say NOT 'C-D' while still truthfully asserting C

Why? Because the statement that there are no A-B's which are also C-D's does NOT preclude the possibility of there being A-B's which are simply C.

__________________________________________________ ____________

a. Some A that are D are C that are B. DOESN'T FOLLOW
"Some females that have x-ray vision are (also) living things that are human."

I think we'll all agree that the premises do NOT support this conclusion. We have no information leading us to believe that there are any such things in existence which satisfy the condition of being both A and D [females having x-ray vision]. Indeed, we have no statement telling us that there are any D's at all!

b. Some C are not D. FOLLOWS
"Some living things do not have x-ray vision."

This follows... since we know for a fact all A are C (all females are living things) and that there exist some A-B-C (there are females which are human which are living things) that are explicitly not D (x-ray vision equipped), there must be C's which are not D. No word yet on whether there ARE actually living things with x-ray vision (in other words, we still don't know if there are C-D's out there).

c. Some B are not C. DOESN'T FOLLOW
"Some humans are not living things."

We have no proof of this. All we know about any Bs is that the only ones we've encountered have been A... we don't even know if there are any Bs which are NOT A... in other words, from the information given we have no idea whether or not there are humans which are not female... and since all females we've encountered are living things, all humans we've encountered are living things as well... maybe there are mysterious humans which are not female and also not living things... I see in illogic the beginnings of a new fundamentalist feminism...

d. Some A are D. DOESN'T FOLLOW
"Some females have the power of x-ray vision."

First off... neither of the premises says anything about the actual existence of things/beings which are D, or have x-ray vision... we have no idea... there COULD be... but we don't know... so we can't suddenly go around asserting the existence of beings with x-ray vision, let alone females blessed with the aforementioned power.

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