Logic Games

loganaldapegarcia

I'm currently looking at a logic game question and one of the following constraints stated: "If J is included in the tour, it must be visited third." My question is: Does the "must" guarantee the J to be 3rd on the tour or does the "if" rule determines the J to be optional?

Sami

The "must" only comes when the conditional statement is triggered. "If" indicates that when the condition arises that J has to be included, then J has to be third.

In this way J has two options.
It's either included and is in 3rd position or its not included.

kimpg_66

You might want to review conditional logic. If is a group 1 logical indicator, which implies "sufficient".

So that rule looks like: J---->J(3)
If J, then J is on 3. So you don't have to have J. Sufficient conditions can be negated every day of the week and it's no big deal (which makes sense: if you don't have J, then there's no way J can be third!). But. If you're going to have J, then it's only option is to be third, because if it isn't on third, then you've negated the necessary which negates the sufficient.

So it would look like this:
J---->J(3)
~J(3)---->~J

Seeking Perfection

   J 

__ __ __ __ | __ __

        J

__ __ __ __ | __ __

If I've got the formatting right, these would be your two options. J is either third in the in group or it is out. I arbitrarilly choose 4 in slots and 2 out, but that kind of information would obviously depend on the other information given. Order doesn't matter in out slots. The other answers are right too, I just thought this might make it more clear.

Edit: the formatting isn't exactly clear, but imagine the J either in the third slot or out.

Additionally, keep in mind that we have the rule
J-->J(3) and of course
¬J(3)-->¬J as @kimmy_m66 explained.

So if we don't have any other rules both possibilities I showed above are an option. If a rule forces ¬J(3) (for example if something else were on 3) we know ¬J. If something forces J we know J(3). If somehow you get both ¬J(3) and J you have a contradiction. Because ¬J(3) gives you ¬J and you can't both have and not have J.

Finally ¬ means not if that wasn't clear.