Neither_nor in the sufficient vs. in the necessary

[niki_lauda]

thus far I have been getting correct answers by treating the word "nor" as simply "and". I am specifically referring to situations were there are multiple sufficient and necessary conditions.

Neither/nor is easy for me to work with when it's in the necessary, primarily because I break the statements apart and make my inferences using the conditional.

However when Neither/Nor is in the sufficient for whatever reason it causes problems for me. So much so that I just use fixed position block rules instead. For example consider the rule:

"Neither oils nor pastels can be scheduled for the same day as lithography"

NOT O
and ----------------------> L
NOT P

when i diagram it this way i can't seem to follow what's going on with the rules. I guess it means that when O AND P are BOTH not selected L MUST be selected. But when I get to Global, Could be true, list games this rule diagram rarely proves useful and I'm always forced to turn to blocks.

Such as:

_O/P_ __L__
__L__ __O/P__

this way of diagramming does prove to be useful. I guess what I'm asking is for future reference, henever Neither/Nor is in the sufficient can I ALWAYS use blocks? When Neither/Nor is in necessary can I always go with the conditional?

[KelseyWoods]

Hi Niki!

For neither/nor rules in the Logic Games, I think you're right that it can often be useful to use the Not Blocks. For the rule "Neither oils nor pastels can be scheduled for the same day as lithography," that just means that you can't have O and L together and you can't have P and L together. That is a perfect rule to diagram with Not Blocks--one showing that you can't have O & L on the same day and the other showing that you can't have P & L on the same day.

Also, be careful with your diagramming. The conditional diagram you showed does not accurately represent the rule. Your diagram basically says that if you don't have O and you don't have P, then you must have L. That is very different from what the rule actually says. A better conditional diagram of the rule would actually be:

L ----> NOT O and NOT P

The contrapositive would be:
O or P ----> NOT L

Again, it's probably simpler to split up the relationships and you could do this with two Double Not Arrows:

L <---|---> O
L <---|---> P

Like with the Not Blocks, this conditional diagram shows that you can't have L and O together and you can't have L and P together.

Remember that just because neither/nor might come at the beginning of the sentence, that doesn't necessarily mean that it is the sufficient condition. Think about the relationship between your conditions to make sure that you are accurately representing that relationship in your diagram.

Whether to use the Not Blocks or the Double Not Arrow diagrams to represent your rule has more to do with how your game is set up. When you have a clear base like in the oils/pastels/lithography game, Not Blocks are a good bet. If your game is a little more undefined or has a lot of conditional rules that you may need to link together, Double Not Arrow diagrams may be more useful.

Hope this helps!

Best,
Kelsey

[niki_lauda]

Kelsey,

thanks. yes I see my notation was incorrect. i should have used rotating blocks instead. no matter the order of the terms L CANNOT appear with either P or O on the same day.

also now that i look back at the pastel example there were no sufficient/necessary indicators given therefore i would use the fixed position rules instead.

using the blocks to diagram this multiple sufficient with "and", is definitely made easier by using the blocks.