Sufficient & Necessary Conditions: “NOT BOTH”

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Alright, so going back to Sufficient & Necessary conditions, we have yet to discuss the “not both” rule on this blog. “Not both” in a sentence implies that at least one of the variables must be absent. For example, I cannot be in both Los Angeles and Berkeley at the same time. I can be in one of these cities, but it is physically impossible for me to be in two different places at the same time.

Let’s take a look at some other examples and draw them out:

1. Naz cannot be at both the Coliseum in Rome and the Eiffel Tower in Paris.

A good way to remember how to diagram this is: If Naz is at the Coliseum, then she is not at the Eiffel Tower.

C - ET

Contrapositive: If Naz is at the Eiffel Tower, then she is not at the Coliseum.


It is very important to remember that the “not both” formula has the positives of the variables as your sufficient conditions and the negatives (i.e. the variable negated) as the necessary conditions as follows:

C - ET


Here’s a great tip: both necessary conditions can be present at the same time, assuming of course that the principle rule and the contrapositive have been correctly diagrammed. Can you see why? Remember, the existence of the necessary condition tells you nothing else (i.e. DON’T JUST REVERSE!!!).

Therefore, in the example above, it can be true that Naz is not at the Coliseum and not at the Eiffel Tower; Naz could be at the Eye of London! Do you see?

Let’s try one more example just to make sure.

2. Naz cannot both keep her eyes open and sneeze at the same time.

So if Naz keeps her eyes open, then she is not sneezing.

EO - S

Contrapositive: If Naz is sneezing, then her eyes are not open.


As you can see, if you line them up, like so:

EO - S


Both necessary conditions can be present at the same time, i.e. it is possible that Naz’s eyes are closed and that she is not sneezing. She can be coughing with her eyes closed! Boom! Lawyered. kinda.

Okay, we have finished reviewing yet another form of Sufficient & Necessary conditions. You know what to do. We give you the tools, and you need to use and weather them. So crack open your LSAT prep app (or book if you are still living in the 20th century) and get to work!

Happy Studying!

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Updated on Sep 28, 2016