Identify what you can properly conclude from the given premises: P: not A → B P: A → not Z P: not Z → F C: ?

Mehran March 22, 2018

Hi @alana, thanks for your post.

This drill is designed to help you feel more comfortable with transitive arguments and sufficient & necessary conditions.

One way to start is to try to combine the given premises.
P2 & P3 can be written as:
A ==> not Z ==> F

OK. Now how can we link in P1?
P1 is not A ==> B.
The contrapositive is not B ==> A.

We can connect this contrapositive with the transitive of P2 & P3, above:
not B ==> A ==> not Z ==> F

Which can be summarized as not B ==> F.
That's answer choice (B).

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

rearden_mettle April 6, 2018

Wow. Thanks Mehran! That really helps. I was using Contrapositives but not associating them as you did in the final diagram. That makes so much sense.

jarebalo20 June 3, 2019

Very helpful, thank you!

Ravi June 4, 2019

@rearden_mettle and @noname, great to see it was helpful! Let us know if you have any other questions—we're here to help!

Kateria February 2, 2022

Very helpful I was so lost before and did not know how to setup the problem. But now I got it.

Ravi February 3, 2022

Happy this helped!