Which one of the following could be the list of the four courses Alicia takes?

on August 14 at 02:51PM

First two rules?

I am a little confused about the first two rules and how they may be different. Rule One says: She Must take Japanese IF she does not take Russian. Ok.. ~R -> J ~J -> R Rule Two says: She cannot take Japanese if she takes MacroE.. M -> ~J J -> ~M In the video, rule one is presented as a not both; or that one of R or J must be in. Is the difference between why we can say that in rule one vs rule two because of the word "must" in the conditional? In rule two, it would seem that J & M certainly cant co-exist, but that they could also both be out...Thanks.

1 Reply

Shunhe on August 19 at 03:20PM

Hi @ElliottF,

Thanks for the question! So I don’t think the first rule should’ve been explained in this way: if she doesn’t take Russian, she must take Japanese. Like you said, that means

~R —> J
~J —> R

But that’s not a “not both.” That means “not neither,” right, since at least one of them has to be in. But you could also have both of them in based on the first rule. So rule one is not a “not both,” it’s a “at least one of the two.”

Now as for rule two, we have if she takes M then she doesn’t take J. Well, as you diagrammed, that’s

M —> ~J
J —> ~M

And this is a “not both” rule, since if you have one, it excludes the other. But you can have neither of them as well.

Hope this helps! Feel free to ask any other questions that you might have.