"People with serious financial problems are so worried about money that they cannot be happy."
P1: SFP ==> not H H ==> not SFP
"Only if their financial problems are solved can they and those around them be happy."
P2: H ==> not SFP SFP ==> not H
Answer choice (B): "People who solve their serious financial problems will be happy."
(B): not SFP ==> WBH not WBH ==> SFP
Solving one's financial problems, i.e. not having serious financial problems, is the necessary condition of P2. We know that necessary conditions do not give us any other information, thus we cannot infer anything from them. Further, remember that the necessary condition of a principle rule and its contrapositive create a viable scenario. Thus, we know that one could solve their financial problems and still not be happy. Therefore, answer choice (B) is not correct.
Answer choice (D): "If people are unhappy, they have serious financial problems."
(D): not H ==> SFP not SFP ==> H
Again, not being happy is the necessary condition of P1. We cannot infer anything else from a necessary condition. Further, we know that we could be unhappy and have no serious financial problems. Thus, answer choice (D) cannot be correct.
Hope that clears things up! Please let us know if you have any other questions.
matthewsaladino96September 20, 2018
Can someone please explain the difference between answer choice C and E.
CeciSeptember 20, 2018
what's the correct answer, if not B?
MehranSeptember 25, 2018
@Ceci (E) is the correct answer here.
(C) is incorrect because it is just negating the principle set forth in the first sentence and we know DON'T JUST NEGATE!
"People with serious financial problems are so worried about money that they cannot be happy."
SFP ==> not H
(C) says, "People who do not have serious financial problems will be happy", which is diagrammed as follows:
not SFP ==> H
This is not necessarily true so (C) would be eliminated.
Hope that helps! Please let us know if you have any other questions.
GoziDecember 12, 2019
How is Naz able to determine (in her explanation of B) that "solving financial problems" is the necessary condition?
Answer choice B says: "People who solve their serious financial problems will be happy"
"...will be happy" seemed to signify a necessary condition to me.
Apparently my diagram must be off due to my misinterpretation of the stimulus. Could you please breakdown the wording in the stimulus and explain to me the words that you consider to be the major signifiers here? That would really help me breakdown where exactly my misunderstanding is taking place.
mprezzyApril 4, 2020
@Naz can you please explain why the second premise "only if their financial problems are solved can they and those around them be happy" is diagrammed as is. I though "only if" introduced a sufficient condition. So I diagrammed thus SFP -> not H. Thanks.
RenatoOctober 5, 2021
@Melissa I'm not a tutor but according to the sufficient and necessary lesson, "only if" introduces a necessary condition; so the statement "only if their financial problems are solved can they and those around them be happy" would be diagrammed as H --> not SFP (correct me if i'm wrong though)
RaviFebruary 5, 2022
@Renato, that's correct! Great diagram. "Only if" introduces the necessary condition.
