Rule Origin Drill, Drill 13, LG workbook

[myverdict]

Page 93, 2015 edition: In the Drill 13: J <------> K

I understood the correct answer, which is 13(D) - Either K is painted and J is painted, or K is not painted and J is not painted. However, my doubt is regarding the 13 (A) - Either K or J, but not both, must be painted.

In the explanation for the answer choices, it is stated that 13(A) produces "J <-------> Not K" diagram. I don't understand how?

As per the lsat/viewtopic.php?t=2626 (Please refer to David Killoran's reply dated Mar 25, 2011 to "Either/Or and the Double Arrow" post, shouldn't the result be

K and not J
Not K and J
If at all, how would this be diagrammed? and,

How can J <-----> Not K be a representation of 13(A)? Please explain.

[Dave Killoran]

Hi Verdict,

Thanks for the question! Let's take a closer look at this one and see what's going on with (A). First, just so it's clear to all readers, answer choice (A) reads as: "Either K or J, but not both, must be painted." Before considering a diagram, what does that statement mean? We know that each time, one of J and K must be painted, but both can't be painted. So, exactly one is painted, and that means there are two possible outcomes from this rule:

• 1. J is painted, and K is not painted;
  
  2. K is painted, and J is not painted.

In other words, all of the following diagrams apply:

• From #1:
  
  J K
  K J
  
  These two diagrams can be combined into: J K
  
  From #2:
  
  K J
  J K
  
  These two diagrams can be combined into: K J. This is just the contrapositive of the first set of statements.

The basic idea is fairly straightforward (one and exactly one of J and K will be painted), and there are various ways to represent that using arrows. J K is one of those representations, and the other is the contrapositive of that super-statement.

Please let me know if that helps. Thanks!

[myverdict]

Yeah, I got it, thanks a lot. I am just doing so much practice on diagramming LG, that I get confused in between sometimes.

[Dave Killoran]

Great, glad I could help! And, don't feel bad at all about not being perfectly clear on this idea right from the start. This is a tricky diagram, and if you haven't analyzed the relationship before it is easy to be confused. The good news is that by asking a question, you now know more about how it works and you've expanded your LSAT knowledge a little bit more. The more hard work you do, the easier this will get, and soon it will be second-nature and you will be able to analyze and diagram any statement with ease.

So, keep up the good work!