Difference Betw'n Double-Not Arrow & Negative Double Not-Arr

[Imcuffy]

I am working on the grouping games at the end of chapter 5. The third game of that chapter states two rules.

The rule states that "Raimundo appears in every photograph that Yakira does not appear in." Based on the explanation, it states that the rule should be diagrammed, Not Y---> R. I mistakenly saw it and thought it should be diagrammed using a Double-Not Arrow because when one is missing the other is present. If I am correct, when there is a negative on the sufficient condition, it CANNOT be diagrammed using a Double-Not Arrow correct? The Double-Not Arrow is only used when there is a negative on the necessary condition. Further, because of the nature of this tricky rule, you resulted in a rule stating:

Not R <--> Not Y.

I do not fully understand this rule.

The second rule states that 'Neither Ty nor Raimundo appear in any photograph that Wendy appears in.' The explanation diagrammed the rule as a Double-Not Arrow. I am assuming again that this is because the negative is on the necessary.

The thing is, I do not know when exactly I can use the Double-Not Arrow versus the Double-Negative Not-Arrow.

[Jeremy Press]

Hi lmcuffy,

You actually do know when you can use the Double-Not Arrow versus what you call the Negative Double-Not Arrow (what we sometimes call the "Double Not-Not Arrow")! You described it perfectly in your post.

The Double-Not Arrow is reserved for conditional rules that have a positive sufficient and negated necessary condition, like:
A B, which becomes A B. This rule means that the variables A and B CANNOT both be IN the group together. At least one of them must always be out of the group. And it's permissible to leave both out of the group.

The Negative Double-Not Arrow is reserved for conditional rules that have a negated sufficient and positive necessary condition, like: C D, which becomes C D. This rule means that at least one of the variables (C or D) MUST always be IN the group. You cannot leave both of them out of the group. And it's permissible to put both of them in the group.

Let us know if that clears up any confusion!