Daily Drills 1 - Section 1 - Question 3

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

MikeND June 9, 2020

Difficult

Can you please explain why choice B is correct? I could not understand it from the explanation.

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Victoria June 19, 2020

Hi @MikeND,

Happy to help!

We are trying to draw a logical conclusion based on the premises outlined in the stimulus.

The first step is to diagram the contrapositives of all the premises.

Not A --> B
Not B --> A

A --> Not Z
Z --> Not A

Not Z --> F
Not F --> Z

The second step is to see if there are any chains that we can make using the transitive property. To do this, two diagrams must have the same N and S condition e.g. Not B --> A --> Not Z

There are two chains that we can make:

(1) Not B --> A --> Not Z --> F
(2) Not F --> Z --> Not A --> B

Answer choice (B) can be concluded from the first chain. Using the transitive property, we can use this chain to conclude that Not B --> F.

Hope this is helpful! Please let us know if you have any further questions.