Conditional Reasoning

[alta]

Hello Powerscore,

I would appreciate it if you could let me know if the following is correct:

A->not B (means that A is not sufficient to get to B; which means that B is not a Necessary condition, it is simply a condition)

not A -> B (means that not A IS Sufficient to get to B, and B is a necessary condition)

Thank You.

[Jeremy Press]

Hi alta,

I'd like you to put a little more flesh on the conditional statements you ask about, because the devil is often in the fine details with these things.

Let's assume the first conditional statement you asked about is part of a game in which we're deciding whether or not to select variables for inclusion in a group. And let's further assume that conditional statement is phrased: "If A is selected to be in the group, then B is not selected to be in the group." We'd diagram such a conditional statement the way you have:
A NOT B.

Your statement that this rule means "A is not sufficient to get to B" is incorrect. Instead, what we'd say is that A is sufficient to tell you that B does not occur. In other words, in our game, A being in the group is sufficient to tell you that B is not in the group. The way we'd ordinarily describe the effect of such a rule in that kind of game is that A and B cannot be together (if you have one, you can't have the other). B's not being in the group is in fact a necessary condition. It's the necessary condition to A's being in the group. Such a rule would imply its contrapositive as well: "If B is selected to be in the group, then A is not selected to be in the group." We'd diagram such a conditional statement as follows: B NOT A.

In your second rule, let's put it this way: "If A is not selected to be in the group, then B is selected to be in the group." We'd diagram that as you have: NOT A B.

Your statement that such a rule means "Not A" (A not being selected to be in the group) is sufficient to tell you B (that B must be selected to be in the group) is correct. A's non-occurrence (A's not being selected) is the sufficient condition. B's occurrence (B's being selected) is the necessary condition. In other words, B's being selected is necessary for A not to be selected. Such a rule would also imply its contrapositive: "If B is not selected to be in the group, then A is selected to be in the group." We'd diagram this as: NOT B A.

I hope this helps!