I’m a little confused with problems were a variable “exists”.
For example, in the drills:
P: X - Y
P: Y exists
P: Z - Y
_________
C: Z exists
Could someone please explain how to reach the answer ‘Z exists’? What happens to the X?
Same with:
P: A - X
P: X exists
P: X - B
_________
C: B exists
Why is the answer ‘B exists’? What happens to the A?
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Hey Katharine, I had the same issue with both of these questions! In the first one, I noticed that the third premise from drill 16 of 32 is actually P: not Z -> not Y. Once I caught this detail. it helped to conclude that Z exists once converted to the contrapositive ( Y -> Z).
What happens to X? We're not sure and thus cannot draw a conclusion about X. Remember that we can't conclude anything from the necessary condition i.e. X-> Y exists. We would be breaking the "Don't Just Reverse Rule" if we said Y exists and therefore X exists (Y->X).
The same explanation applies the the second example. To be brief, we are not sure what happens to A and thus cannot mention it in the conclusion. We can conclude that if X exists then B must also exist.
I could be totally wrong here, but this is what made sense to me.
It would be great if @Ravi or one of the 99th percentile mentors could validate just to be certain.
