#6 - Global, Rule Substitution

[Jon Denning]

The final, sixth question for the first game is undoubtedly the toughest, as those preceding it were all quite straightforward, and #6 is an oddball of sorts: a Rule Substitution question.

While not necessarily the hardest thing you'll see in LG, they are among the most unique, in that they typically occur at most once per test (if at all; although as we'll see this particular exam had two!) and ask you to replace one of the original rules with an answer choice that would yield an identical game situation. That is, produce this exact same game with all of its consequences and inferences and possibilities and Not Laws and interactions by means of a swap, where you'd put an answer in place of a rule and never know the difference.

I won't go into a full breakdown of this type here—although I think you'll find this question analysis helps you better understand them—however if you're reading this as a PowerScore course student or an owner of the Logic Games Bible, there is a lengthy discussion of these questions in the LGB, and in the L11 Homework/Supplemental area in the Online Student Center for the Full-length and Live Online classes.

The rule we're asked to replace in this question is rule 3, where K and F cannot have the same theme. So the first thing you want to do is consider the effects of that rule, both immediate and secondary.

The immediate effect is that K and F must be different, with one getting and R and the other a U, and the secondary/inferential effect is that both G and H are Rs. So any answer choice that allows K and F to be the same is instantly eliminated, as are any that let G or H or both be U.

Also, you can't have an answer that imposes conditions that weren't a part of the original rule set, where something that was allowed under the original rule no longer is. In short, everything needs to stay exactly the same as before. More freedom of movement, or less, instantly eliminates an answer.

Here though that notion of K and F potentially being the same (and thus breaking the original rule) actually takes care of all of them:

Answer choice (A), with H getting R, is out for this reason: K, F, and H could all be Rs, with G and J as Us.

Answer choice (C), with F and J different (meaning F is an R), is out, too: K, F, and H could be Rs, with G and J as Us.

Answer choice (D), with J immediately after an R, tells us nothing about the other assignments. For instance,
putting J in 2 after H in 1 as an R could still see G as a U in 3, with K and F both as Rs in 4 and 5. Other arrangements
also exist that would violate our original conditions.

Answer choice (E), where K is the same as either G or H but not both, could, like (A) and (B), let K, F, and H be Rs,
with G and J as Us.

Since each of those allows for our initial rules/restrictions to be broken, none is functionally equivalent to what we started with!

And what about B?

Answer choice (B) duplicates our original construct: if G and H are both Rs, and J is always a U, that leaves
one R and one U for K and F, our two remaining variables. That means they can't be the same, and we're back
where we started. So here we've replaced the rule just using its big inference!

Sometimes you have to go a step further and consider almost third-level inferences that the original rule created (like if that rule had been the trigger for templates, the correct answer would need to be as well, etc). But here we're off the hook for anything that in-depth.