Q8 - Some students attending a small

[kmewmewblue]

I wonder if I could ignore the first statement.

"Some students attending~live off campus."

Because I find the assumption without this statement.
MM=Music Major, C=Choir, OFF=Live off Campus

MM→C
-------
OFF→/MM (contrapositive:MM→/OFF)

Missing assumption is MM→C→/OFF

So what kind of affect this first statement does is only to confuse us? Or am I missing something?

[noah]

..what kind of affect this first statement does is only to confuse us? Or am I missing something?

Indeed, you can ignore that sentence. And extra information is ALL OVER the LR section. What you've done is boiled down the argument to its core. That's the key to tackling assumption family questions.

I like your clean approach on this, and the heavy conditional logic makes it a smart one.

In case someone else is looking for a full explanation, here goes (borrowing some of yours!):

This sufficient assumption question involves some rather clear use of formal logic. One approach is to just dive in:

MM=Music Major, C=Choir, OFF=Live off Campus

MM→C
-------
OFF→/MM (contrapositive:MM→/OFF)

Missing assumption is MM→C→/OFF

That's exactly what (A) gives us.

Another approach, if you were able to "get" the stimulus, is to see that the professor jumps from choir to off campus, so the answer has to connect those. And, specifically, we need to learn that if you live off campus, you're not a choir member.

A quick challenge - can anyone see why this isn't a necessary assumption, but it is a sufficient one?

As for the wrong answers:

(B) is a premise booster - we already know that music majors are in the choir.

(C) is a distraction. We don't care about folks that are not music majors. We want to know if being a music major or choir member means you live on campus.

(D) doesn't tell us anything about the folks off campus - are any of those folks music majors?

(E) simply strengthens the connection between the music majors and the choir members. We already know they're connected. We don't need the relationship to be bi-directional.

[haejun.rim]

..what kind of affect this first statement does is only to confuse us? Or am I missing something?

Indeed, you can ignore that sentence. And extra information is ALL OVER the LR section. What you've done is boiled down the argument to its core. That's the key to tackling assumption family questions.

I like your clean approach on this, and the heavy conditional logic makes it a smart one.

In case someone else is looking for a full explanation, here goes (borrowing some of yours!):

This sufficient assumption question involves some rather clear use of formal logic. One approach is to just dive in:

MM=Music Major, C=Choir, OFF=Live off Campus

MM→C
-------
OFF→/MM (contrapositive:MM→/OFF)

Missing assumption is MM→C→/OFF

That's exactly what (A) gives us.

Another approach, if you were able to "get" the stimulus, is to see that the professor jumps from choir to off campus, so the answer has to connect those. And, specifically, we need to learn that if you live off campus, you're not a choir member.

A quick challenge - can anyone see why this isn't a necessary assumption, but it is a sufficient one?

As for the wrong answers:

(B) is a premise booster - we already know that music majors are in the choir.

(C) is a distraction. We don't care about folks that are not music majors. We want to know if being a music major or choir member means you live on campus.

(D) doesn't tell us anything about the folks off campus - are any of those folks music majors?

(E) simply strengthens the connection between the music majors and the choir members. We already know they're connected. We don't need the relationship to be bi-directional.

Would it be possible for there to be 2 sufficient assumptions here?

1) Not C--> OFF and its contrapositive: Not OFF--> C
2) C--> Not off and its contrapositive Off and Not C

[citadelroman]

I'm still rather confused on how we figured out the missing assumption. I don't get how the missing assumption fits into the rest of the question and would appreciate a more in-depth, step-by-step explanation. Thank you!

[deedubbew]

Even the assumption (0-->~C) is an sufficient condition, it still contradicts a premise: C some O. Although, I did choose the right answer because all the others were horrible, I had to go back and still didn't understand how it could be possible for both conditions to coexist. Help appreciated =D

[christine.defenbaugh]

Even the assumption (0-->~C) is an sufficient condition, it still contradicts a premise: C some O. Although, I did choose the right answer because all the others were horrible, I had to go back and still didn't understand how it could be possible for both conditions to coexist. Help appreciated =D

Great question!

I think you may be misreading a premise! The first sentence does not tell us that some of the choir members themselves live off campus. Instead, it simply tells us that some students live off campus (and that the university has a cool choir). We don't actually know anything about these off-campus students!

What do you think?


Also, here's a slightly different way to visualize the logic that Noah and kmewmewblue discussed above. Since this is a Sufficient Assumption question, we want to fill in all the gaps to guarantee the conclusion:

CONCLUSION: Music Major -----------------------------> NOT off campus
PREMISE: Music Major-------->Choir Member

(A) fills in the gap we need by connecting Choir Members to NOT off campus. Adding this in we'd get:

Music Major-------->Choir Member------->NOT off campus

Then the conclusion would be totally valid!

Would it be possible for there to be 2 sufficient assumptions here?

1) Not C--> OFF and its contrapositive: Not OFF--> C
2) C--> Not off and its contrapositive Off and Not C

The first of these is not a sufficient assumption. Just because all the non-choir people live off campus, that doesn't mean that there can't ALSO be choir members off campus! This would not allow the professor to validly conclude that all the music majors live on campus.

I hope this helps clear up a few things!

[deedubbew]

Oh. My. Gaw. Before you pointed me in the right direction, I re-read that sentence so many times and didn't understand that it was referring to students at a university which happens to have a well-known choir rather than choir students attending the the university. I feel like if another similar question had grammar like that I'd fall for the same problem. It sounds to me like the students who attend the uni and are with the choir, live off campus. Do you have any suggestions for avoiding grammar misinterpretations like this? It's not the first time, I've had trouble with this kind of grammar.

[roflcoptersoisoi]

Students <----- some-----> ~ Live on Campus
Music Major ----------------> Member of choir

---------------------------------------------------------------
~ Live on campus -------> ~ Music major

~ Live on Campus -----> ~ Music Major ---> Member of choir.

(A) ~ Live on Campus --> ~Member of the choir. Bingo.
(B) Music Major ---> Member of choir. Restatement of premise.
(C) Live of campus <----s----> ~ Music major. "Some" is not strong enough to substantiate the conclusion. Even if it said "all" students that live off campus, it would be wrong because it's a mistaken reversal of the assumption
(D) Live on campus ---> music majors. Mistaken reversal of assumption
(E) Member of choir ---> music major. Reversal of existing premise