Ch. 9: Conditional Logic 202 Question

[kiransfatima]

This may seem nitpicky, especially since these types of statements are rare, but...

On p. 326 there is the example, "If neither Ted nor Seth is selected, Raj will be." It is represented at -T and -S --> R

However, I thought it would be -T or -S --> R, with the contrapositive as -R --> T and S. You see, if the statement was "if either Ted or Seth," then it would be T or S. Because the statement is "neither Ted nor Seth," wouldn't it be -T or -S? I'm confused in the logic.

[ohthatpatrick]

Neither/nor can be translated as "not-this AND not-that".

If I tell you that in the U.S., 10 year old children can neither legally vote nor legally purchase alcohol, I don't mean that a 10 year old has to choose between voting or buying alcohol. I mean that BOTH are prohibited.

If I handed you a piece of cake and told you, "I've put neither arsenic nor anthrax in this cake", again, you are expecting BOTH of them are not in there, not one or the other.

It's confusing, since 'nor' rhymes with 'or', but neither/nor rules out two things.

Let's look at the example you cited,
"If neither Ted nor Seth is selected, Raj will be."

Let's say that Ted is selected but Seth isn't.

Is the rule triggered?

No. It would be false to say that 'neither Ted nor Seth is selected'. Ted IS selected!

If Ted isn't selected AND Seth isn't selected, NOW it's true to say that neither Ted nor Seth was selected.

Hope this helps.