Diagraming either/or statements

[saranash1]

I don't understand how these are different than sufficient and necessary conditions. In the course book on page 210 it shows examples with diagrams that appear to be exactly the same as the ones for sufficient and necessary conditions.

[David Boyle]

I don't understand how these are different than sufficient and necessary conditions. In the course book on page 210 it shows examples with diagrams that appear to be exactly the same as the ones for sufficient and necessary conditions.

Dear saranash1:

They are diagrammed similarly to sufficient-and-necessary condition diagramming, since they are a form of it, you could say. However, there is some elaboration, since "either/or" is tricky.
As noted on p. 210, on the LSAT, "either" tends to mean "at least one of the two", although both could be included. Thus, in the example given, "slash John arrow Jack", or "slash Jack arrow John". But both guys could attend the party.
And there are further variations given, e.g., on pp. 210-211, about "general outside knowledge" issues, and on pp. 211-212, the "either...but not both" construction, which seems to follow the usual meaning of "either", i.e., "one but not the other".
You may want to read that whole 3-page section again and see if you have any other questions. Again, the "either/or" thing is a special subset of sufficient-and-necessary diagramming, which is why it looked so familiar. Hope that helps.

[acp25]

Hello!

How do I know which one is the NOT side of an either/or statement?
Question # 2 on page 2-62 of the test prep states:

Either Jones or Kim will win the election.

I answered - Jones (J), Kim (K)

J NOT K
K NOT J

But the answer in the book is

NOT J K
NOT K J

Is the sufficient automatically the NOT item on an either/or statement?

[AthenaDalton]

Hi acp25,

Thanks for your question!

Keep in mind that, unless otherwise specified, an either/or sentence like this has three potential outcomes: (1) John wins the election and Kim loses; (2) Kim wins the election and John loses; OR (3) both Kim and John win the election. The third outcome could occur, for example, if both were running for a multi-person board that had three seats. The statement "either John or Kim will win the election" means at least one, but possibly both, could win.

So the best way to diagram to account for the possibility of both John and Kim winning is to state that, if John didn't win Kim must have won or, if Kim didn't win John must have won:

JW KW
KW JW

If we were told in this question that only one person could win the election, then the diagrams you initially used (JW KM and KW JM) would also be correct.

This is an example of the LSAT differing a bit from real life, since in normal conversation we use "either / or" to suggest that only one thing or the other could occur, but not both. On the LSAT, either / or means one or the other will occur, or both.

A more detailed explanation of diagramming either/or statements, along with additional examples, is included on page 2-52 of the Lesson 2 Homework.

I hope this makes sense, and good luck studying!

Athena Dalton

[jessamynlockard]

Hi,
I wanted to check my understanding. It was really hard for me to read "Either Jones or Kim will win the election" and not assume "either one, but not both could win" because of how I implicitly think about elections.

My general question is how common is it for the LSAT will trick us with this? I imagine in Logic Games, the wording would be sufficiently clear. Would this type of thing be most likely to come up in logical reasoning?

My specific question is how to diagram if "Either Jones or Kim will win the election but not both". That would be a biconditional, right? J K

[Jonathan Evans]

Hi, Jess,

Confusing conditional clues and precise logical terminology are common on more difficult games; while I couldn't cite the likelihood that this particular situation will arise on an upcoming LSAT, you should parse carefully any statement containing such language.

Sometimes it is necessary to learn how language is used on the LSAT, especially when such usage is at variance with conventional diction. As Athena noted above, there is a detailed discussion of this particular topic in the second lesson (it is also covered in Chapter 6 of the Logical Reasoning Bible, page 208).

Just remember that there are two common meanings of "or" in common parlance:

1. The "exclusive 'or'": You can have the cake or the pie (but not both).
2. The "inclusive 'or'": If you are a teacher or a government employee, you are entitled to a 10% discount off your purchase.

This latter "inclusive 'or'" is how "or" must be understood on the LSAT. What if you're both a teacher and a government employee? You would expect to qualify for the discount!

Thus if you encounter "or" between two options on the LSAT, understand the implicit "or both."

It takes some practice, but I'm confident you'll get the hang of it. You may even find yourself taking advantage of this new understanding in your day to day life. "Would you like cake or pie?" "Yes, thank you. I'll have both!"

Re your question about diagramming:

My specific question is how to diagram if "Either Jones or Kim will win the election but not both". That would be a biconditional, right? J K

This statement would be diagrammed:

J K
K J
J K

You would need all three in this case because exactly one of them must be selected. It is not possible that neither K nor J is selected.

I hope this helps!