missing premise drill

I need help with this question P: X---->Z P: Z does not exist P: ? C: A Exist

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Nic_geraci September 15, 2019

Not X —> A

BECAUSE... If Z doesn’t exist then you must use the contrapositive of X—->Z which is Not Z —> Not X so to complete the problem it MUST be Not X—> A

That reads as Not Z—> Not X—> A

Irina September 21, 2019

@shazia khan,

The question requires us to find a missing premise. We are given the following premises:
(1) X -> Z
(2) ~Z
(3) ?
(4) Therefore, A

We can take a contrapositive of (1):

(4) ~Z -> ~X

Then from (2) and (4), we can infer:

~X

Now, the only remaining step is to get from ~X to our conclusion A, the missing premise thus must be ~X -> A

If we put all the resulting premises together:
~Z
~Z -> ~X
~X ->A

We can conclude that:

A

Let me know if you have any further questions.