P: A → YP: B → CP: ?C: not Y → not B

SeanC April 25, 2021

Explanation

I’d like to know how to come up with the answer “Not A > Not C” as opposed to “A > C”

Replies

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Gabriel July 13, 2021

I have no idea... I figured since it's the reciprocal that's just how it is.

December 12, 2021

I'm having the same issue

Jay-Etter January 24, 2022

Hi everyone,
So if we write out conditional and their contrapositives:
A -> Y //Not Y -> Not A
B -> C // Not C -> Not B
Missing premise
Conclusion: Not Y -> Not B

We want to start with not Y in our conclusion so let's grab the contrapositive of our first premise
Not Y -> Not A
We want to end with Not B so let's grab contrapositive of P2
Not C -> Not B

Now we just need to connect the two, so we need Not A -> Not C
Then we get Not Y -> Not A -> Not C -> Not B
And we can simplify that to our conclusion Not Y -> Not B

So our missing premise is Not A -> Not C. Note that we could also give the contrapositive, C->A.
Hope this helps, feel free to follow up with further questions.

Danielle May 2, 2024

Hi, I am still unsure of why these are the specific steps to follow to find the missing conclusion? Can you explain the logic to me as I am not following along well with this explanation. Thanks.

Danielle May 2, 2024

Hi, I am still unsure of why these are the specific steps to follow to find the missing conclusion? Can you explain the logic to me as I am not following along well with this explanation. While I understand we are following the transitive property, I fail to understand why the correct answer is the contrapositive of C--> A ...