# Philosopher: A person is morally responsible for an action only if that action is performed freely. And an action is ...

Ryan on September 12, 2019

Why is E correct? Why is C incorrect?

Thanks

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Skylar on September 28, 2019

@Ryan-Mahabir Happy to help.

The first thing we should notice is a significant amount of Sufficient and Necessary terminology in the form of "only if." This indicates our need to diagram the statements and find their contrapositives. We know that "only if" introduces Necessary, so our diagrams should look like this:

MR -> F
not F -> not MR

F -> AAO
not AAO -> not F

AAO -> not W
W -> not AAO

We see that we can use the transitive property to combine the diagrams as follows:

MR -> F -> AAO -> not W
W -> not AAO -> not F -> not MR

(E) is the correct answer choice. It uses the term "unless," which introduces the Necessary condition and requires that we negate the Sufficient condition. Therefore, it is diagrammed as: F -> AAO (which we already know must be not W). This matches the second diagram we initially made, so we know that it must be true.

(C) is diagrammed as AAO -> MR. This is incorrect because it reverses the correct order of the variables. If we look to the transitive chain we made, we see that we can say MR -> AAO and not AAO -> not MR, but that's all we can do with those two variables. Therefore, it does not follow that AAO -> MR must be true.