## pt34 s2 Q10 Formal Logic help

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eddie3636

Posts: 19
Joined: Wed Aug 22, 2012 5:28 pm

### pt34 s2 Q10 Formal Logic help

I understand why all of the other answers are wrong but cannot see how (D) is correct.

The assumption is: ~LD then ~SN, SN then LD however, D (if I am translating correctly) says: LD then SN, ~SN then ~LD. All I did here was follow the only=if rule.

My thought is that the question is equating LD and SN, however this would seem to make A the correct answer.

Any help on this would be greatly appreciated.

Eddie

sighsigh

Posts: 263
Joined: Wed Oct 20, 2010 8:47 pm

### Re: pt34 s2 Q10 Formal Logic help

eddie3636 wrote: however, D (if I am translating correctly) says: LD then SN, ~SN then ~LD.

You got that part wrong. D is saying 'students with special educational needs => students with learning disabilities' (SN => LD). You might've gotten confused between notating 'only' and 'the only.'

'Only A are B' is notated B => A, while 'The only A are B' is notated A => B. 'Only' indicates a necessary condition, and 'The' indicates the condition is applied to the latter term, not the former.

_____________________________________

Students with learning disabilities => ~have enrolled in school
---
Students with special educational needs => ~have enrolled in school

Sufficient (and necessary) assumption:
Students with special educational needs => students with learning disabilities

(D) contains this in its answer.

Daily_Double

Posts: 1031
Joined: Tue Dec 04, 2012 8:45 pm

### Re: pt34 s2 Q10 Formal Logic help

eddie3636 wrote:The assumption is: ~LD then ~SN, SN then LD however, D (if I am translating correctly) says: LD then SN, ~SN then ~LD. All I did here was follow the only=if rule.

My thought is that the question is equating LD and SN, however this would seem to make A the correct answer.

Ok, so we have an S/A here. Usually formal logic is in MBT questions, but this is a good thing, so we know that the S/A will link the premises to the conclusion. Let's look at the stimulus and find the core:

CORE: The school is violating it's charter.

Why?

(p1) Student body --> Some kids with special needs
(p2) no kids with learning disabilities have enrolled.

Ok, at this point, I'm prephrasing an answer. My prephrase would be "If no kids with learning disabilities are enrolled then no kids with special needs are in the student body. There's really not any formal logic here. This is just cookie cutter conditional logic. Anyways, your issue is between A and D. Let's see what we have.

A: learning disabilities ---> special need. This reverses the logic. We need if NOT learning disabilities enrolled ---> NOT special needs in student body. Or I guess we could be looking for the contrapositive: Special needs in student body ---> learning disabilities enrolled. But because this is an early one, I'm expecting the correct answer to be the exact same as my prephrase.

D: special needs---> learning disability. This is the contrapositive of my prephrase. If we insert that into the premises we have:

CORE: The school is violating it's charter.

Why?

(p1) Student body --> Some kids with special needs
(p2) enrolled ---> not learning disability
(S/A, Answer D) special needs---> learning disability

So linking the logic, we have (combining p2 and Answer choice D):
enrolled ---> not learning disability ---> not special needs

Now combining this with (p1), we have:

enrolled ---> not learning disability ---> not special needs ---> not Student body

I'm not exactly sure, but I'm guessing you misinterpreted answer choice D. You're correct in using the phrases "only, only if, requires, etc." to signify the necessary condition. However, the condition isn't the phrase immediately after those words; it is the phrase that the words refer to. In this case we have, in answer choice D, educational needs ---> learning disabilities. Because the only refers to learning disabilities.

For example, the only people with drinks in there hands are people with demanding jobs. What this example, and answer choice D are saying is that the only people who do A are B. You would translate this example, in conditional form, to:

drinks in hands ---> demanding jobs.