Biconditionals -- Chaining vs Splitting?

BlindReviewer

This has come up briefly before on the forums, but I wanted to ask more about chaining biconditionals rather than splitting. On PT 54 game 1, because I wasn't on point with my understanding of biconditionals, I tried to chain up the first two rules with the rest, and it ended up being a total mess. I was super confused, whereas when I came back to it and just split the board and got rid of the biconditional it was a lot easier.

I think there are times where chaining biconditionals is helpful, but my real question is, do we then have to write two versions of it when trying to read the chain? Because biconditionals can be /A <-> B or A <-> /B, (and the other two for "always together"), I find it pretty hard to read the chains. How do you guys go about this / is it ever really THAT helpful? It seems like if a biconditional comes up on an in-out game, it's always better to split it?

Also if you know of any games that use chaining biconditionals, that would be helpful!

BlindReviewer

For anyone following this thread -- Game 4 of PT 39 is an example of where you would chain the biconditionals, but it really helps to chain it here rather than split O and P into different boards.

MIT_2017

I don't want to give you a cheesy cop out answer..... but I really do think it is entirely personal preference of how you want to represent the rule. Just use whichever method feels most natural when you encounter that situation in a game -- I wouldn't harp on it too much.

Lucas Carter

PT 41 Game 3 has one!!

BlindReviewer

https://7sage.com/lsat_explanations/lsat-49-section-1-game-3/

The problem set here for in/out games has been really helpful, and I think @MIT_2017 you're right in that it comes down to personal preference, but I guess it just comes down to whichever is going to be easier/more time efficient. It's turning out to be much harder to practice than I anticipated!

If anyone knows of any other good in/out games aside from those in the problem set that would also be really helpful.

Lucas Carter

@BlindReviewer said:
https://7sage.com/lsat_explanations/lsat-49-section-1-game-3/

The problem set here for in/out games has been really helpful, and I think @MIT_2017 you're right in that it comes down to personal preference, but I guess it just comes down to whichever is going to be easier/more time efficient. It's turning out to be much harder to practice than I anticipated!

If anyone knows of any other good in/out games aside from those in the problem set that would also be really helpful.

A great one to try that is not included in that list is PT 57 Game 3.

Jonathan Wang

I generally think it's right to say that it doesn't matter as long as whatever you do works for you, but I figured I'd add my two cents anyway: the more I work with biconditionals the less I like chaining them. My major problem with chaining is that it sacrifices usability for elegance. In a pressure environment, I would much rather have usable diagrams than pretty ones (a lot of times there's an overlap, but I'm not convinced this is one of those times).

Here's an example. A -> B <-> C -> D looks nice and neat, so great. Now, let's say I give you not-B (/B). Are you going to remember to take the contrapositive to the left (/A) and ALSO the contrapositive to the right (/C), given that the other 99% of the time you do conditional statements you do the logic strictly left to right and contrapose right to left? Consider now if you had split it up into A -> B -> C -> D and then C->B separately. In this new scenario, is it easier or harder for you to notice that you have to take both contrapositives?

Since you should be able to execute any 'normal' looking conditional statement in your sleep, it's really just a question of balancing - is the added elegance of the diagram worth the extra hoop you put up in front of yourself? With biconditionals, because the alternative is to split it into two single conditionals (that, again, you should be able to execute in your sleep), I personally think the answer is no. Again, your mileage may vary.

To be clear, 99% of the time it IS very helpful to recognize a biconditional exists because they're very powerful rules that usually lead to tons of consequences (it's very high on my pecking order of rules to look to when trying to understand a game). I'm just saying it may not be helpful to force yourself to represent it as one in the conditional chain if it's going to mess with your ability to read and understand the relationships properly. Never forget that notation is a means to an end, not an end unto itself.

Tangent - for the same reason, I differ from JY a bit on the last question of the birds in a forest game (in/out game #1 in the curriculum). He likes representing the new rule H -> /S by drawing a left-running arrow from the existing H in the middle of diagram to the existing /S at the front of the diagram. It's neat, elegant, conforms well to the existing diagram, and works fine if you can read it properly. The issue is that if you're used to reading conditional statements from left to right and have it drilled into your head that in any given conditional S -> N, S is on the left and N is on the right, it's not a given that you'll read it right.

BlindReviewer

Wow I have been touched by greatness -- thanks @"Jonathan Wang" !

As a side note, for anyone drilling in/out games -- for PT 58 game 4, though it's not a biconditional, when you link up the web of conditional chains, you end up with M as an odd piece. Just splitting the boards on M (one for M in and one for M out) was significantly more helpful than any kind of chaining, because I didn't have to look at M going into two directions in the conditional rules. (Just thought that was similar to what Jonathan says above.)