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Otherwise & Not Otherwise Biconditionals

jasminesadejasminesade Alum Member
edited March 2019 in Logical Reasoning 249 karma

Hey there! Hope everyone is doing well in their LSAT studies!

I stumbled upon a question that stated "otherwise" within the answer choices. (for reference: PT 63 Section 1 #21) J.Y. noted that otherwise means "or, and not both" which is a biconditional, however, I'm having trouble distinguishing this from "not otherwise"

If someone can kindly look over the two statements I have provided below, one with otherwise & the other with not otherwise.


  1. If a class involves science work, the class will be conducted in a laboratory; otherwise, it will be conducted in a normal room.

  2. If a class involves science work, the class will be conducted in a laboratory or a normal room, but not otherwise.

Are these both the same in conditional logic? Laboratory <--> Normal room.

Also, would someone be able to provide an example that would likely be a rule on a logic game with those terms?

Thank you!


  • Michael.CincoMichael.Cinco Member Sage
    edited March 2019 2116 karma
    1. SW --> L


    NOT(SW) --> N

    If L and N are your only options (ie Not L = N)

    then NOT SW --> Not L (N)

    If you combine that with the Contrapositive of the Original you get Not L --> Not SW
    And Not SW --> Not L and that is indeed a bi conditional Not L <--> Not SW and the logical Equivalent SW <--> LW

    So otherwise just negates the sufficient condition to get you a new necessary condition, it can only become a bi-conditional if Not L = N

    1. SW --> L or N

    But not Otherwise:

    Not SW --> Not ( L or N) [which is (Not L and Not N)]

    Take the contrapositive of the above and you get

    N or L --> SW

    combine with the first statement and you get your bi conditional

    N or L <--> SW

    Not Otherwise is indeed a bi-conditional without further assumptions.

    I hope that helps

  • Michael.CincoMichael.Cinco Member Sage
    2116 karma

    Also I do recall seeing a rule in a sequencing game that used the otherwise language.

    Those with better memories than I do can probably point out that game.

  • jasminesadejasminesade Alum Member
    249 karma

    thank you for your explanation!

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