@Halle-Diaz for the conclusion to be Not Y ==> Not B, you must also recognize that B ==> Y. To get from B ==> C and A ==> Y to B ==> Y, you need the intermediate premise that C ==> A. Answer (A) says that A ==> C, but that does not produce the same result. However, since the contrapositive of Not A ==> Not C is C ==> A, it is the correct answer as it allows you to make the full argument that B ==> C ==> A ==> Y.
Does that make sense?
LSATChrisSeptember 19, 2019
How do I know I need premise C====>A I suppose I'm not fully grasping the transitive property.
IrinaSeptember 19, 2019
@LSATChris,
We are given a set of premises with one premise missing and are asked to identify a missing premise that would allow the conclusion to be inferred.
(1) A-> Y (2) B -> C (3) ? (4) Therefore, ~ Y -> ~B
First, let's identify common elements in the premises and the conclusion. We can see that there is Y and ~ Y on lines (1) and (4). How do we infer ~ Y from Y? We can take a contrapositive of (1):
(5) ~Y -> ~ A
Then we have B and ~ B on lines (2) and (4). We can take a contrapositive of (2) to get a ~B inference:
(6) ~C -> ~B
Let's put all our inferences together:
(5) ~ Y -> ~ A (6) ~C -> ~B ?
(4) Therefore, ~Y -> ~B
How do we get from ~ Y - > ~ A and ~ C -> ~B to ~Y ->~ B? We must connect ~A and ~ C:
(7) ~ A -> ~C
Now we have the following premises:
~ Y -> ~ A ~ A - > ~C ~C -> ~B
and can conclude that ~ Y - > ~A -> ~C -> ~B or ~Y -> ~B
Let me know if this makes sense or if you have any further questions.
lsatdandyAugust 10, 2020
Awesome explanation. I finally got it. The key here is via use of contrapositives leading to the need to inject ~C to the linear sequence expressed by the conclusion: ~Y ==> ~B. thank you so much.
