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

Irina October 22, 2019

@Kelly,

The question requires us to use the rules of inference to determine the conclusion that follows logically. We are given the following premises:
(1) ~A -> B
(2) A -> ~Z
(3) ~Z -> F

First, let's start by identifying common variables. Premise (2) and (3) both contain ~Z, which means we can form the following chain:

A -> ~Z -> F which is logically equivalent to:
(4) A -> F

Next let's use transposition (contrapositive) so we have a common variable in premise (1) and premise (4) above:
(5) ~B -> A - transposition (1)

Now we can combine premises (4) and (5) into the following chain:
~B->A-> F which is equivalent to:
(6) ~B -> F

which represents our conclusion.

Let me know if this makes sense and if you have any further questions.

cglee February 12, 2020

Wow! That is pretty intense.

cglee July 8, 2020

@Kelly I seem to be having a problem with the missing conclusion drills.
please see below:

Missing Conclusion Drill Question:
P: A--->X
P: X exists
P: X--->B
C: ?
I did a chain, I found that "X" was my common variable. Chain was: A--->X--->B
I know if I have A that is sufficient for the necessary X, I also know that X is sufficient to give me the necessary B. My thought was the conclusion would be A--->B, the weird part for me is I know B exists because of the sufficient being X. How far off base am I in my reasoning?