Diagramming Formal Logic statement

[LSATmaniac2.0]

Dear Powerscore,

I am reviewing PT 63 right now and came across question 15 in section 1, concerning Hagerle and whether or not she has to pay for damages. There is a bit of Formal Logic at work, nothing complicated in the question itself, but answer choice B has me a bit confused. I got the right answer, but I find I cannot diagram the formal logic in the answer choice. "If someone tells the same lie to two different people, then neither of those lied to is owed an apology unless both are". How would I diagram that? If A B unless C? If NOT C NOT B?

I would greatly appreciate the help.

LSATmaniac2.0

[Laura Carrier]

Dear LSAT Maniac,

You are certainly not alone in finding a sentence like this one—with nested necessary conditions—tough to diagram! Fortunately, nested conditions don’t occur too frequently on the LSAT—but when they do, the key to handling them effectively is simplification.

Along those lines, you could apply the Unless Equation to the original necessary condition to transform it into this:

Apology Owed to Either Apology Owed to Both

Thus we know that, if someone tells the same lie to two people, if either of those lied to is owed an apology, then both are. This would allow you to create a diagram like this:

Tell Same Lie to Two People (Apology Owed to Either Apology Owed to Both)

Or, more abstractly:

A (B C)

Which feels a little easier to interpret than your original version. But better yet, when you encounter a nested conditional statement like this, what you really want to do is to make it as easy to interpret as possible, which can be helped by thinking about the sentence more substantively than formally.

Here, we are really being told that owing an apology is a necessary condition to telling the same lie to two people, but only under certain circumstances: only if (or not unless) it is owed to both. In other words, we can think of this sentence as containing only a single necessary condition (apology owed), which is itself subject to an exception in the circumstance where an apology is not owed to both people.

To simplify even further, this would mean that, if someone tells the same lie to two people, they either owe an apology to both or they don’t owe an apology to either. Which we could diagram in a more familiar format, without changing the meaning of the sentence:

Tell Same Lie to Two People Owe Apology to Both OR Don’t Owe Apology to Either

When you encounter a nested conditional, you can often transform it into an “and” or an “or” in order to eliminate the extra condition, and if so, I would say that this is the best way to diagram it.

I hope this makes diagramming these nasty sentences a little easier!
Laura

[LSATmaniac2.0]

Dear Laura,

Thanks for the help. I am still trying to work through the logic myself, to see if I can get there in my own head.

So far I've gotten here:
if same lie neither is owed, unless both are

The unless both are neither is owed becomes:
~both owed, then neither owed

This statement's contrapositive breaks down more literally into:
~neither owed (meaning if A is owed AND B is owed, OR A is owed but B isnt, OR A isnt but B is) then both are owed (A + B).

More simply, if someone is owed, I'll make it a positive letter not a negative one, so:
If A + B, OR A + ~B, OR ~A + B A + B.

Then I plug that back into the original and I get:
If same lie If A + B, OR A + ~B, OR ~A + B A + B.

But that is confusing me. What do I do now with the statements? I figure that there are only 2 outcomes on the unless side of the equation. Either A + B OR ~A + ~B. So, I'm supposed to take the results of such an if then and plug it into the original equation?

If same lie A + B OR ~A + ~B

Does that make any sense, the way I did it?

Much appreciated,
LSATmaniac2.0

[Adam Tyson]

I would suggest focusing less on the diagram (which, while intended to simplify, can often just confuse things) and focusing more on the substance, as Laura was saying. Forget the arrows and the negation signs and all the symbology and get to the heart of the matter, which is "all or nothing". You either owe it to both or you don't owe it to either. While we love to teach about diagrammatic tools to help clarify and more easily deal with complex relationships, sometimes they get in the way and obscure rather than clarifying, and this looks to be one of those cases. Dump the diagram and deal with the substance and you should find this one much easier to deal with.

Good luck!