@jonesali001 the first step is writing out all the premises and contrapositives:
A ==> M Not M ==> not A Not x ==> J Not J ==> X X ==> not M M ==> not X
Now, we're looking for chaining together multiple statements, in other words, connecting multiple ==> together. So looking at the answer choices, we first need to validate that we have a statement that will include both sides of the ==>.
So:
(A) J ==> A, you can see we have NEITHER a statement with J ==> nor ==> A, so we won't be able to link the two.
(B) not J ==> A. We have a statement with not J ==>, but not one with ==> A, so we can't link these two.
(C) not J ==> not A. We have both a statement with not J ==> and one with ==> not A, so we're off to a good start. Now how would we actually connect the two? We can chain like this: not J ==> X ==> not M ==> not A. So (C) is correct.
I hope that helps!
shmemMay 27, 2019
but aren't the opposites of the premises the contrapositives? so if not A ==> not M then A ==> M
?
RaviMay 28, 2019
@shmem,
The contrapositive of not A - >not M isn't A - >M; it's M - >A. To get the contrapositive, you negate each side of the arrow and switch the sufficient and necessary conditions.
Does that make sense? Let us know if you have any other questions!
StevenJanuary 13, 2022
Wow! @Max-Youngquist
That explanation gave me the epiphany I've been waiting for. Great job! Thank you so much.
