Bi-directional arrow

[mbmoss]

[christine.defenbaugh]

Thanks for posting, mbmoss!

Hmmm - I'm not familiar with the book that information appears in.

From what you've posted, all of the inferences depend on only the "J-->K" half of the double arrow. Because of that, there is no difference in the inferences that you can make when you replace the double arrow with "J-->K". Of course, if you were to replace it with "J<--K" you would be in serious trouble - you would lose ALL your inferences!

If you think about it, this makes sense. "J<--K" is not useful in this situation because there's nothing (other than J) that leads to K, and there's nothing (other than K) that J would lead TO.

Double arrows, or biconditionals, can absolutely be useful, since you really have two statements at the same time. As such, they can give you a lot more information than only one statement or the other - in the right situation.

If I had to guess, without further information, I'd say that whoever wrote the book you have was trying to illustrate that, and simply chose a poor example.

I hope that helps clear it up a bit!