Identify what you can properly conclude from the given premises:P: A → MP: not X → JP: X → not MC: ?

wannabelawyer April 6, 2017

Help please!

I am confused why it's not j to not a rather than j to a. Please explain!!!

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Mehran April 21, 2017

@wannabelawyer J ==> A would be incorrect.

J is your necessary condition in P2 so J's existence tells you nothing else (remember, don't just reverse!).

The existence of the sufficient condition guarantees the existence of the necessary condition.

Let's take a closer look at how we would properly combine these premises.

We would combine these premises as follows:

A ==> M ==> not X ==> J

This chain is created with P1 (A ==> M), the contrapositive of P3 (M ==> not X) and P2 (not X ==> J).

The contrapositive of this chain would be:

not J ==> X ==> not M ==> A

So we are able to conclude:

A ==> J
not J ==> not A

So (C) would be the correct answer.

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

ericahlevine May 1, 2018

This was extremely helpful