One of the most important rules of mapping premises is that you cannot solely negate the sufficient and necessary conditions when attempting to create the contrapositive. Rather, you must negate and reverse the conditions.
Therefore, the contrapositive of answer choice B (A - > not C) would be C - > not A as opposed to answer choice E which reads not A - > C.
Therefore, the correct mapping for the question is:
P: A - > not B which has the contrapositive of B - > not A
We are looking for the missing premise which allows us to conclude that B - > C.
We know that B - > not A, so the missing premise is not A - > C or answer choice E.
Hope this is helpful! Please let us know if you have any further questions.
icontrer19May 14, 2019
That makes sense but why can it not be C then? Where it says C -> not A?
RaviMay 15, 2019
@icontrer19,
Great question. (C) and (E) mean fundamentally different things.
(C) is C - >not A, and (E) is not A - >C
We need not A to be in the sufficient condition so that the chain properly links up. The contrapositive of (E) is not C - >A, and this is completely different from (C).
P: A - >not B (B - >not A) P: C: B - >C
if we have something go from not A to C, then we can conclude B - >C
A - >not B (B - >not A) not A - >C
B - >not A - >C
C: B - >C
Because (C) has the sufficient and necessary conditions mixed up, there's no way we could conclude B - >C if we used (C) as the missing premise.
Does this make sense? Let us know if you have any other questions!
