Modality

So far we’ve dealt with if then statements that are categorical: No Great White Sharks are vegetarians. Now we’re adding a level of complexity with some, all, and most. This level is called modality.

This video is 11 minutes long, and it’s all vital information.

(3:08 in video) Negation of All

You would think the opposite of all would be none, but it isn’t. The opposite of all (which you are going to be using often on the GMAT if you are taking the contrapositive of an all statement) is some are not.

All just means 100% of something.

Some means greater than 0% (none) but not 100% (all).

Some are not means less than 100% (all). It could mean 0% (none).

“Life is a great adventure or nothing”
-Helen Keller

Explanation

The contrapositive (show in red above) shows that the opposite of nothing is something (the opposite of nothing isn’t everything).

Some or not means everything less than all, including nothing. So, on the GMAT, saying he has some or not winning lottery tickets in his pocket is perfectly valid (even if he has none).

(5:58) Converse of All

The converse of All statements isn’t valid
All dogs (D) are nice animals (NA)
All D => NA
Doesn’t mean that nice animals are all dogs.
NA => D is invalid.

The negation of All is Some are not.

The negation of All dogs are nice animals is NOT No dogs are nice animals, but “Some Not“: Some dogs are not nice animals.

Note: “Some are not” could mean zero.

The opposite of nothing is some.

(7:11) Modality w/Venn Diagrams

All grad students are higher-ed students.
Some grad students are on financial aid.

At Beverly Hills University,
no students are on financial aid.

Rule #1: All A are B
All GMATs are hard tests.

Contrapositive (valid):
Some tests that are not hard are not an GMAT.

Converse (invalid):
All hard tests are GMAT tests.

Inverse (invalid)
Some GMATs are not hard.
(maybe the June one?).

Rule #2: Some A are B
Some law school programs are part-time.

Valid Inference: Some B are A
Some part-time programs are law school programs.

Invalid Inference: Some A are not B
Some law school programs are not part-time.

Invalid Inference: Some B are not A
Some part-time programs are not law school programs.

Premise 1: Some voters view Hillary unfavorably.
Premise 2: Some voters view Trump unfavorably.

Conclusion?

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This can be a confusing question, but all it’s really asking you to do is just use substitution (athletes for bankers).

Video Questions

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