When Does “Either/Or” Mean “Both” on the LSAT?

Hi Ellis,

Thanks for the question! The phrase “either/or” ALWAYS means both unless it is specifically stated that it doesn’t, or if the two conditions are jointly known to be unable to occur together. If you have the LSAT Logical Reasoning Bible, take a look at page 196 in the 2017 edition–I talk about how Either/Or works in detail there, and then reference thereafter in several spots in the book.

So, if you have a phrase such as “Either A or B occurs,” then you can have the following outcomes:

* A and not B
* B and not A
* Both A and B

The one thing that is impossible is “neither A nor B.” This all occurs because “either/or” is basically identical to “at least one” in meaning.

Now, the test makers can eliminate that “both” possibility one of two simple ways:

1. Add a specific prohibition against “both.”

For example, a phrase could state, “Either A or B occurs but not both.” In that case, only the following two outcomes are possible:

* A and not B
* B and not A

2. Alternately, they could use public domain/common sense information to exclude the possibility of both, for example:

“On Friday, I am going to spend all day either in Los Angeles or in Paris.”

Well, Paris and Los Angeles are two cities that do not geographically overlap, and so to spend the day entirely in one means that you automatically cannot spend the entire day in the other; in other words, only two outcomes to the statement exist:

* All day in Los Angeles and not in Paris
* All day in Paris, and not in Los Angeles,

So, the bottom line is that “either/or” always means “both” unless you have one of the situations above.

Please let me know if that helps. Thanks!

Hi Aubrey – interesting question. I’m going to say “yes” to keep things simple and just consider the black/white distinction in terms of single, object color, rather than anything to do with skin tone or ethnicity ( the “you are…” part, since, as people, we come in many shades and could certainly be of multi-racial heritage).

From an LSAT perspective you would see it more along the lines of something like, “Every dog in the dog show was either a solid black or a solid white color. All of the poodles in the show were white.” So what must be true? “No black dogs were poodles.” What’s a trap answer? “All of the white dogs were poodles.”

In other words the situation will either (1) be given where it’s physically impossible to have both conditions at once (simultaneous coexistence cannot occur)—you can’t be in Florida and Kentucky simultaneously, for instance—or (2) be presented in a way where one or the other condition MUST be the case—you were either born in Florida or you were not—or (3) be clarified by provided context that shows it’s an either/or situation, like my dog example in the previous paragraph.

Failing those though you need to keep an open mind to the possibility that both things could potentially happen together, or that neither thing is occurring (some third, unmentioned option might exist instead; this is the mistake behind a False Dilemma flaw).

I hope that helps!

Hi Lea – thanks for the question! This is an interesting one, for sure!

First, and before I get to the notion of creating multiple diagrams, it’s always important to understand the context of the game scenario when interpreting rules.

That is, for the messages example we’d want to know first and foremost if it’s possible for more than one person to leave a single message (go into the same spot in 1-5). If it is possible–and in that example it seems clear that it would be–then the “or” rule has to be taken to potentially include “both” until you’re explicitly told “but not both.” (Conversely, in a game where every space has just a single variable, then an “or” rule naturally includes “but not both,” since “both” is never an option)

So for the half brother OR grandmother rule, you’d want to show H/G since that’s a guarantee, but in theory a number of uncertain things could still occur: H and G together, H or G with someone else, H or G alone…

And then for the second rule example that includes “but not both” then clearly you can’t have H and G together in that spot…but you could still have quite a number of other things happen: H or G alone, as well as H or G with someone else. That’s a bit more restrictive of course, but the possible “doubling” in a position still leaves things a touch uncertain, or “fluid” (albeit somewhat less so than the simple “or” rule) as you’ve described it.

Which leads to your question about templates (showing both options of H and G in 1). Each rule creates a split path based on spot 1, so in theory each could produce templates where you have H in 1 and another with G in 1. The only difference being that the second rule wouldn’t allow a template with HG in 1.

But that duality isn’t sufficient to justify making diagrams for each! What would need to happen, and could occur with either rule option honestly, is that the individual templates should create additional, significant inferences, filling in some sizable portion of the rest of your setup. So if H in 1 doesn’t force anything else to happen, then creating a diagram based on it would be both time-wasting and pointless. On the other hand, if H in 1 (for either rule option) leads to a number of other spaces filling in, then it’s far more likely to be worth showing/pursuing and templates may make sense.

I wrote about this idea in another article if you’d like to take a look! https://blog.powerscore.com/lsat/lsat-logic-games-how-and-when-to-create…

So the short answer to all of this is that either rule option *could* produce useful templates, with the second (“but not both”) rule proving a touch more restrictive in doing so, but the choice to commit to templates requires additional inferences that neither rule by itself would necesssarily produce.

I hope that helps!

I would just like to ask the part where you say when there is a specific prohibition against “both.”
For example, a phrase could state, “Either A or B occurs but not both.” In that case, only the following two outcomes are possible:
* A and not B
* B and not A

‘But not both’ and ‘but not otherwise'(they are equivalents, right?) would indicate a bi-conditional here then?