Supply the missing premise that makes the conclusion follow logically:P: X → YP: ?C: X does not exist

MsHonesty December 29, 2016

Why C doesn't work

if we have X -> Y and Y -> not X. which is equivalent to X -> not Y and we can't find such X i.e. X doesn't exist.

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Mehran January 4, 2017

@MsHonesty thanks for your message but I am not sure I am understanding your question here.

(C) does not allow us to properly conclude that X does not exist.

(B) on the other hand does by invoking the contrapositive of our premise:

X ==> Y
not Y ==> not X

"Not Y" is the sufficient condition of our contrapositive which leads to the necessary condition, i.e. X does not exist (or "not X").

Hope this helps! Please let us know if you have any other questions.