P: Y → CP: ?P: A → not BC: B → C

Ravi February 27, 2019

@yuetngan,

Happy to help.

We have

P: Y - >C

P: ?

P: A - >not B

C: B - >C

Let's take the contrapositives of the given premises and see how we
might be able to link them together

Y - >C
/C - >/Y

A - ->not B
B - >not A

We know our conclusion is B - >C, so how can we go from B to C?

The contrapositive of our second premise is B - >not A and our first
premise gives us Y - >C. What if we bridged these premises by putting
in not A - >Y? This would allow us to conclude B - >C

Y - >C

not A - >Y

B - >not A

Combining these, we have B - >not A - >Y - ->C, and we can conclude

B - >C.

Looking at the answer choices, we don't see not A - >Y. However, we do
see its contrapositive, which is not Y - >A. We see this with (B), and
it's the correct answer choice because if we add this premise, we can
properly conclude that B - >C.

Does this make sense? Let us know if you have any other questions!

JenS December 12, 2020

Hello,

I've reread the explanation above a few times and I'm still confused on the part of bridging the premises. I don't understand how you got to ~A --> Y since Y is in the sufficient in the first premise and ~A is in the necessary in the contrapositive of the second premise.