Conditional - Neither/nor

[jbrieger]

How do I diagram a neither/nor statement, and what would the contrapositive be?

[tomasag]

SHORT ANSWER: Depends... how's the actual question worded?

LONG ANSWER: It could be a double arrow or a double-not arrow or, since I'm certainly no expert, maybe something altogether different. Yikes! For starters, I would suggest pp. 246-247 of the Logic Games Bible (i.e. Ch. 5 - Group Games, The Double Arrow).

It uses this example: "A will be selected if and only if B is selected." (I reworded slightly because I'm not sure if I'm allowed to copy verbatim.) This is to be diagrammed as follows:

A <---> B

Further, it states that only two scenarios are possible under this relationship:

(1) A and B are both selected; or

(2) Neither A nor B are selected.

I think (2) might address your question; HOWEVER, the double-not arrow (p.244) also incorporates that latter possibility.

For example, "If A, then not B." Ultimately, this results in the following diagram:

A <-|-> B

In this relationship three scenarios are possible:

(1) If A, then not B;

(2) If B, then not A; or

(3) Neither A nor B.

CAVEAT EMPTOR: I'm not a staff member, so I would perhaps wait on confirmation of my response's accuracy by a member of the staff before accepting it. Regardless, good luck!

[Jon Denning]

Actually tomas that's a solid response! The one thing I might add is that in much of your discussion, the "neither/nor" is a part of a result of initial statements (which might not be exclusively neither/nor in nature). If you are diagramming a statement that includes neither/nor, then the exact diagram will depend on how it is stated (is it a straight "Neither A nor B occurs," or is it part of a larger statement, such as "If A occurs, then neither B nor C occurs" ?), but ultimately neither/nor is about saying that "not both" of them occur.

The second trick to neither/nor is just recognizing the contrapositive, and that NOT BOTH is negated by either/or.

So "if A then neither B nor C" would be:

A NOT B and NOT C

And the contra would be:

B or C NOT A

And that's really it! Let me/us know if you have questions!

Jon