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February 15, 2016

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

When Does "Either/Or" Mean "Both" on the LSAT

Understanding the proper conditional relationship represented by the “either/or” conjunction in LSAT questions is crucial in both Logic Games and Logical Reasoning questions. While there are some solid rules you must follow, ultimately you should take into account the context in which the phrase is used.

Learning the Rules

Typically, a rule such as “either A or B must be selected” is inclusive. It allows for the possibility of selecting both A and B (unless the rule specifically precludes that by stating “either A or B must be selected, but not both”). Thus, at least one of A or B must be selected:

LSAT conditional reasoning help

However, compare this rule to the following:

  • Mary has a higher LSAT score than does either Kate or Jane.

Whenever this wording is used (“than does either” or “than either”), we can infer that Mary’s LSAT score is higher than either of the other two girls’: i.e. Mary has a higher score than both of them. In this case, “either” requires the use of the conjunction “or” to make the sentence is grammatically correct.

Sample Problems

Let’s take a few examples.

In the statements below, “either…or” means “both”:

  • Anne arrives earlier than does either Bob or Cathy.
  • Jack is a better chess player than is either his mentor, or his opponent.

By contrast, in the following statements “either/or” does not necessarily mean “both,” and just means “at least one”:

  • Anne arrives before Bob or before Cathy.
  • Jack is either a better chess player than his mentor, or a better chess player than his opponent.

Finally, in the statements below, “either/or” precludes the possibility of “both”:

  • Anne arrives before either Bob or Cathy, but not before both.
  • Jack is either a better chess player than his mentor, or a better chess player than his opponent, but Jack is not a better player than both his mentor and his opponent.

The point of this discussion is that you must be very careful when you see the “either/or” construction, and you cannot assume that it always means “at least one, possibly both.” As we have seen, there are certain circumstances when it means just “both,” and there are times when the test makers throw in additional language to eliminate the possibility of “both.” Always read very closely, and you will be rewarded when the test makers go beyond the normal usage!

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Posted by PowerScore Test Prep / Conditional Reasoning, LSAT Prep / Conditional Reasoning, LSAT Prep 7 Comments

  • Ellis
    March 18, 2017 at 7:22pm

    Hello I have an example that’s giving me a little trouble, wondering if anyone could explain it for me? It’s in my lesson book for formal logic but I’d appreciate further explanation if anyone can 🙂

    Why can either mean both in this case?

    Sylvia will serve either falafel or veggie burgers at her cookout.

    If no falafel -> veggie burgers
    if no veggie burgers -> falafel

    explanation given – this statement establishes a minimum of one of these menu items. Sylvia must serve at least one of the two foods; she may also serve both.

  • Dave Killoran
    March 22, 2017 at 5:28pm

    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!

  • Aubrey Hepler
    January 17, 2018 at 10:36pm

    The same would apply to “You are either black or white”?

  • Jon Denning
    January 18, 2018 at 1:27am

    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!

  • Lea Washington
    June 07, 2018 at 5:02pm

    Hello and thanks so much for this article/post. I’m studying LSAT Logic games and this post is helping me understand the issue better. Just wanted to get a clarification for a scenario like this one:

    “Kendra comes home to find that there are 6 messages left on her voicemail by 5 people.
    Rule 1: Her (H)alf brother OR (G)randmother left the first message.”

    In this case, I should diagram this rule like so? Correct?
    “Message 1: H/G. (Meaning H or G in this first msg slot)”

    Now if the question said:
    “Rule 1: Her (H)alf brother OR (G)randmother left the first message, but NOT BOTH,”
    Does that mean that I should pick which one would permanently stay in this slot? So should I decide eventually based on the future questions for this game whether the half brother or grandmother gets that slot?

    If I need to explain this in a different way let me know.
    I’m just trying to figure out when I need to write more than one diagram to represent multiple outcome possibilities, or if the game is asking me to eventually pick just one possibility for diagramming. I’m having trouble deciding what positions are permanent and what’s fluid lol.

  • Jon Denning
    June 07, 2018 at 8:06pm

    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!

  • Lea Washington
    June 13, 2018 at 8:27pm

    Thanks so much Jon!

  • SJ K
    June 15, 2018 at 5:53am

    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?

  • Dave Killoran
    June 19, 2018 at 3:26pm

    Hi SJ,

    Yes, you are correct! It becomes the following two bi-conditionals (which are contrapositives of each other):

    A <—–> Not B
    Not A <—-> B

    Those both get across the idea that exactly one of A and B is selected.

    Well done!

Comments

  1. Liana says

    March 21, 2025 at 10:41 am

    thanks for info.

    Reply
  2. Ryan says

    October 16, 2020 at 12:54 pm

    Can you help me understanding when either / or is used in a boolean statement? Such as:

    Either A or B can be used to accomplish task C.

    Is the statement true or false, when there is knowledge that A cannot accomplish task C?

    Reply
    • Dave Killoran says

      October 19, 2020 at 12:08 pm

      Hi Ryan,

      Thanks for the message. A situation such as the one you describe would only occur on the LSAT after knowing the either/or statement was possible, for example as part of the rules of a logic game. Later information, such that A cannot accomplish task C could be added, but that would only limit posibbilities; it would not make the initial either/or statement false.

      Thanks!

      Reply
  3. Sarah says

    May 25, 2020 at 2:15 pm

    If the word only either is used?
    For eg there was a question saying
    O is greater than either of K and atleast greater than one of L.
    In this “or” isn’t used.
    Hence in this question will either be used as k1 or k2 or both k1&k2?

    Reply
    • Jon Denning says

      May 26, 2020 at 10:34 pm

      Hi Sarah – thanks for posting!

      I’m not sure I fully understand what you’re asking here. Any chance you could point me in the direction of the question/example you’re referencing so I can read it directly (as originally written)? That might help clear things up on my end, and give me a better chance of helping you out 🙂

      Thanks!

      Reply
  4. Emily says

    August 2, 2019 at 8:36 pm

    Where is the section on “either/or, not both” in the 2018 Bible? I’ve looked all over and can’t find it.

    Reply
    • Dave Killoran says

      August 3, 2019 at 6:19 pm

      Hi Emily,

      The discussion of Either/Or begins on page 208 of the 2018 LRB edition 🙂 There’s then a summary on page 232.

      Thanks!

      Reply

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