P: A → CP: C → BP: not BC: ?

gixer750 September 21, 2016

Please help explain this one

I did all the work right(wrote it down, found the contrapositive), but I don't see how not b- not c- not a means not a like the answer.

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Mehran September 23, 2016

@gixer750 no problem! Let's take a closer look:

P1: A ==> C
not C ==> not A

P2: C ==> B
not B ==> not C

From these two principles, we can create a chain using the transitive property as follows:

A ==> C ==> B
not B ==> not C ==> not A

P3 tells us that "not B" exists.

Remember, the principles in P1 and P2 and the chain we created from them are conditional statements, i.e. "if A, then C."

We need to know something else to invoke these principles.

"not B" invokes the contrapositive of P2 and allows you to conclude "not C."

"not C" invokes the contrapositive of P1 and allows you to conclude "not A."

So "not A" would be the correct answer here.

Hope that helps! For a more in-depth discussion of these concepts, please watch our video on Sufficient & Necessary conditions.

kdkennamore January 30, 2018

Not C isn't an answer choice.

Mehran February 4, 2018

Yes, we know "not C" is not an answer choice. "Not A," however, is. Please read our prior explanatory post carefully.

marthajanidsilva September 19, 2019

How come the isn't ( Not B - Not A) ? The chain shows both variables

Starr-Latimer June 20, 2021

I don't understand how the correct answer is just "not A" instead of "not B -> not A"