P: X → CP: ?C: A–some–C

mystah August 9, 2021

Logic chain

Can someone explain the steps to get this answer? I am lost and sant figure I it what I’m doing wrong

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September 15, 2021

Hello,

Premise 1: X --> C
(contrapos: not C --> not X)

Premise 2: Unknown

Conclusion: A - some - C
(Contrapositive: C - some - A)
Remember: "some" quantifiers like this one do not need to be negated for the contrapositive, just flip it around

Now you can combine the first premise and the conclusion. This is what you get when you do that:

X --> C - some - A

Since X is C and some C's are A's, that means that some X's are A's too. You can shorten this chain to:

X - some - A
This is not an answer choice, but if you take the contrapositive:
A - some - X

Now you have the answer!
Hope that helps you!

carolineoneal February 14, 2022

that helped!

Lisandra July 6, 2022

Thank you!

Kristina November 12, 2023

I am diagraming these the right way but am not understanding the order when it comes to the variables and the final answer.

I see the correlation after diagraming but get the variables in a different order sometimes. For example, on this question my diagram showed " x -> c -> some a. Is there a rule that I am missing?

Emil-Kunkin November 13, 2023

I think that the diagram you mentioned would be valid here since some statements are reversible