Additive Inference Drill #1 and #6

[myverdict]

The first question: Some As are Bs, No Bs are Cs, All Cs are Ds

I understood the inferences that A---some---not C & D---some---not B. I also made an inference that A---some---not D. Can you please tell me why the 3rd inference is not possible?

As A---some---not C, shouldn't A---some---not D also be an inference?

Similarly, with the sixth question: Some Ns are Os, No Os are Ps, No Ps are Qs, All Qs are Rs.

I understood the inferences that N---some---not P & R---some---not P. However, I also made other inferences that N---some---not Q & R---some---not O. Can you please tell me why the 3rd and 4th inferences are not possible?

[Dave Killoran]

Hi MyVerdict,

Thanks for the question! the relationship in question appears as:


A B C D


You got two of the inferences correctly, but have run into trouble on a statement that is not an inference. Let's see why.

You correctly inferred that: A C. As we know, we also have C D. Trying to combine those two may be a problem, because C and C are different terms and can't be combined. In other words, any inference chain can always be written out in its individual pieces and then combined to create the inference. Here, the causes a problem because it introduces a negative along the supposed chain, on C. when that occurs, I can't combine the statements, and the result is no inference.

Using that logic, take a look at the second question you ask about. Those two arrows in the middle of the diagram create a blockage that we can't jump across. Why? Because P is actually negative in relation to O ( O P ) but positive in relation to Q (P Q ). In other words, it's a different term, but the arrows allow us to connect it all together into a single chain. As an exercise, break that chain down into single statements and see if you can draw the inferences you proposed. You won't be able to!

The beauty of this is that you have encountered this while still practicing, and once you lock this idea down you will become even better as a test taker.

Please let me know if that helps. Thanks!