Identify what you can properly conclude from the given premises: P: not A → B P: A → not Z P: not Z → F C: ?

queenvoldy November 25, 2017

Same.. what's the - - in between the letters for??

Mehran November 27, 2017

Hi @queenvoldy, please see our previous reply to you explaining the use of diagramming in formal logic for LSAT success.

Hey @Jess, thanks for your post. This drill is testing your ability to understand formal logic diagramming, the difference between positive and contrapositive statements, and when transitive conclusions might be validly drawn therefrom.

The drill presents three premises:
P: not A ==> B
The contrapositive (CP) is:
CP: not B ==> A

P: A ==> not Z
CP: Z ==> not A

P: not Z ==> F
CP: not F ==> Z

Answer choice (B) is a valid transitive argument combining the premises as follows:
CP P1 + positive P2 + positive P3
not B ==> A ==> not Z ==> F
combined, the transitive is:
not B ==> F

Hope this helps! Please let us know if you have any additional questions.

Victoria-O. June 6, 2020

How do I know when to combine the contrapositive and the positive premise? That's the part that confuses me after I negate all of the premises. How do I know where to go from there? How would I know that Not B ==>A would be the first in the chain?

Skylar June 28, 2020

@Victoria-O., happy to help!

After you find the contrapositives for all of the given premises, you should look for premises that have variables in common that we can combine using the transitive property. This means that the common variable should be the necessary condition in one of the premises and the sufficient condition in the other.

Here, "A" is the necessary condition in the contrapositive of our first premise and the sufficient condition in our second premise. Therefore, we are able to combine the premises to make a larger chain.

However, do not worry if you did not start at this exact point. There are multiple routes you can take to arrive at the same answer. For example, you may have noticed that Z is the necessary condition in the contrapositive of our third premise and the sufficient condition in the contrapositive of our second premise. We can combine these statements to create a chain that will then connect to our first premise. This forms the contrapositive chain: not F -> Z -> not A -> B, which simplifies to: not F ->B. The contrapositive of this is: not B -> F. Both of these statements are equally correct as our missing conclusion.

Does that make sense? Hope it helps! Please let us know if you have any other questions!