Sufficient & Necessary Conditions: “EITHER/OR”

I know your LSAT prep sometimes feels like it is very sufficient and necessary heavy. And why wouldn’t it be? After all, you will encounter sufficient and necessary on both Logical Reasoning and Logic Games, which is three out of the four sections! So, I thought, how about we go over another type of sufficient and necessary sentence!

Today I’d like to review either/or. You know the type: Either A or B.  With either/or sentences, a good way to remember how to diagram is to just pick a variable, and negate it. That negated variable is your sufficient condition and the other is your necessary condition! Let’s go ahead and try it out:

1.     Either Naz will do the dishes, or she will take out the trash.

Okay, pick a variable: Naz will do the dishes. Now negate it! This will be diagramed as: If Naz does not do the dishes, then she will take out the trash.

D - T

Contrapositive: If Naz does not take out the trash, then she will do the dishes.


Remember, we can read both necessary variables together as a possible situation. In this case we see that Naz can both take out the trash and do the dishes. “Either/or” means at least one, and therefore it can include both. That is a big deduction that most of my LSAT prep students forget. The “necessary variable situation” is very important to remember, because it is commonly tested by LSAC.

D - T


Let’s try another:

 2.     The cookie will either have vanilla icing on it, or it will have chocolate icing on it.

Okay let’s choose a variable: have vanilla icing on it. Negate it! So we have: If the cookie does not have vanilla icing on it, then it will have chocolate icing on it.

V - C

C ? V

Remember, again, in this situation, it is possible for the cookie to both have chocolate and vanilla: think about the classic black and white cookie! Look to the cookie Elaine!

Remember that the simple “either/or” sentence is very different from the “not both” sentence. Go back over the “not both” blog post and compare!

Okay, you are now armed with yet another sufficient-necessary strategy my young LSAT prep-padawon, may the logical force be with you!

Happy Studying!

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