@Melissa this is another Strengthen with Sufficient Premise question so we are looking for the answer choice that 100% guarantees the conclusion (i.e. the super premise).
But before we look at the answer choices, let's break down the stimulus.
The conclusion here is: "None of the students who live off campus is a music major."
We know that none is treated just like "No As are Bs" so this conclusion is diagrammed as follows:
LOC ==> not MM MM ==> not LOC
How do we know this? The premise is: "All music majors are members of the choir."
"All" introduces a sufficient condition so this premise is diagrammed as follows:
MM ==> MC not MC ==> not MM
So this is our argument after we extract the pure logic from the stimulus:
P: MM ==> MC not MC ==> not MM
P: ?
C: LOC ==> not MM MM ==> not LOC
I hope this setup reminds you of our "Supply the Missing Premise" daily drills.
There is clearly a gap here. To close it, we need to connect being a member of the choir (i.e. MC) with not living off campus (i.e. not LOC) as follows:
MC ==> not LOC LOC ==> not MC
This missing premise guarantees the conclusion as shown with the following transitive property:
MM ==> MC ==> not LOC LOC ==> not MC ==> not MM
(A) says, "None of the students who live off campus is a member of the choir."
(A) is diagrammed as follows:
LOC ==> not MC MC ==> not LOC
This is exactly the missing premise we set forth above, so (A) is the correct answer.
Hope that helps! Please let us know if you still have questions on any of the other answer choices here.
judybaladiMarch 11, 2019
Why is D incorrect?
Jacob-RMarch 12, 2019
Hi @judybaladi
As Mehran discussed in his answer above, the ultimate conclusion of the professor is that none of the students who live off campus is a music major. This gets diagrammed as:
C: LOC -> not MM MM -> not LOC
We also have another premise: that all music majors are members of the choir.
MM -> MC Not MC -> not MM
So what bridges that gap? Answer A, because it tells us that none of the students who live off campus is a member of the choir.
LOC -> not MC
Which, when linked with our other premise, gets us from LOC -> not MC -> not MM, which (an abridged version) was our conclusion: LOC -> not MM.
So why was answer D wrong? Answer D did not allow us to bridge that gap. Answer D can be diagrammed as follows:
LON(!)C -> MM
Note that this answer tries to trick you because it could easily be mistaken in symbolic logic/quick reading for live OFF campus.
But because it is a premise about living on campus, we don’t have the right pieces to link the gap between living of campus / being a music major. (In other words, it could be entirely true that all students who live on campus are music majors, but maybe some students who live off campus are also music majors. So we haven’t properly drawn the professor’s conclusion.)
I hope that helps! Please let us know if you have further questions.
