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

osnapitzkenzie March 23, 2016

Not Quite Understanding

I'm reviewing the explanation of the question and the logical reasoning still isn't quite clicking. I don't follow the method of how I was supposed to come to that conclusion based on the information given.

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Mehran March 29, 2016

@osnapitzkenzie this is the transitive property. You can combine the premises given as follows:

not B âž¡ï¸ A âž¡ï¸ not Z âž¡ï¸ F

This chain is created using the contrapositive of P1 and then P2 and P3 as stated.

This allows you to conclude: not B âž¡ï¸ F

You can also conclude the contrapositive, i.e. not F âž¡ï¸ B, as follows:

not F âž¡ï¸ Z âž¡ï¸ not A âž¡ï¸ B

This chain is created using the contrapositives of P2 and P3 and P1 as stated.

Hope this helps! Please review our Sufficient & Necessary lesson for a more in-depth discussion of these concepts.