We're missing C in the premise, and how can we conclude B - >C?
If we look at the contrapositive of the first premise, we have B in the sufficient condition, which matches B being in the sufficient condition in the conclusion.
What if we linked up not A to C? not A - >C
Then, we'd have
B - >not A not A - >C
We could combine these to form
B - >not A - >C
And we could conclude B - >C.
You asked why the missing premise isn't A - >not C. Let's take a look at what that would do
P: A - >not B B - >not A
P: A - >not C C - >not A
Can we conclude from these two premises that B - >C? No, we can't.
We have A going to not B and A going to not C with the originals, and with the contrapositives we have B going to not A and C going to not A. Nowhere do we have the B - >C link that we're looking for, so A - >not C doesn't work as our missing premise.
Does this make sense? Let us know if you have any questions!
