Otherwise & Not Otherwise Biconditionals

jasminesade

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.

Examples:

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.Cinco

1. SW --> L

Otherwise

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.Cinco

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.

jasminesade

thank you for your explanation!