Flawed Parallel Reasoning Questions - - Question 31

Not all tenured faculty are full professors. Therefore, although every faculty member in the linguistics department ...

tselimovic November 10, 2014

Clarification

Is Not All diagrammed the same as Not Both? Thanks!

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Naz November 14, 2014

No they are not diagrammed similarly.

Let's take for instance: "Not all A are B."

This means that at least one A is not B, correct? And at least one means "some."

So we would diagram this: A-some-not B

Now let's think about a "not both" statement.

"At least one of A or B will be in, but not both."

So if A is in, then B is out and if B is in, A is out:

A ==> not B
B ==> not A

Then we have a third option of "either/or" with "not both."

"Either A or B is in, but not both."

We diagram this in two parts: "Either/or"

Not A ==> B
Not B ==> A

"Not both"

A ==> not B
B ==> not A

Hope that clears things up! Please let us know if you have any other questions.