5/5 with two 4 stars!!

From a more mathematical perspective…

Negation is distributive, and when the negation acts on ANDs and ORs, they switch.

Example:

Let’s assume our financial state is one of these four:

• Rich

• Comfy

• Poor

• Broke

Rich is then logically equivalent to (could be replaced by):

not comfy AND not poor AND not broke

So then, NOT Rich is logically equivalent to:

not (not comfy AND not poor AND not broke)

Using the distributive property of the negation (just as a negative multiple is distributed through parenthesis) and the AND to OR rule…

Not Rich = comfy OR poor OR broke

Assuming we can only have one financial state at a time, we can clearly see that the negation of Rich is not poor, but any other state besides Rich.

@GraysonCogswell Garfield is not unique for being a cat, but he is an instance of a member of the set of all cats.

So for any generic thing, x, if x is a member of the set of all cats, it is a cat, which implies it is also a member of the set of all mammals in this case.

The criteria for being a member of the set of all cats then necessitates membership in the set of all mammals.

Equivalently then, this logically implies that if a generic thing x is not a member of the set of all mammals then it must also not be a member of the set of all cats.

I find the formal mathematics version of this more helpful to read for the Garfield example. It would be written as such:

• For all generic things; if that thing is a cat then it is a mammal

• Garfield is a cat

• Therefore, Garfield is a mammal