Q20

[samiraa180]

Is there a systematic way to deduce that K and T cannot be selected together.

I've translated the rules below:

NO FH
NO NT

if H--->K

~K --->~H

if K---> N

~N----> ~K


So is there a way to deduce answer choice "C" ahead of time? I vaguely recall a method where the rules are combined in such a way that it becomes obvious that certain entities cannot be selected together, but I couldn't remember which step to take first.
And is there a way to make sure that i've deduced all the entities that cannot be together? So in a nutshell, can a step-by-step guide be provided? Thanks in advance.

[fmuirhea]

The first two rules can actually be rewritten as conditionals themselves. Think about N and T: if we know that we cannot select them both, what happens if, for example, we do select N? T would be out. What if we select T? N would be out. So, we actually have this relationship:

N ---> ~T
T ---> ~N

You can now add this information about N and T to the chain you already have:

H ---> K ---> N ---> ~T
T ---> ~N ---> ~K --> ~H

(Once the FH rule is reconstructed in this way, you could add it to the chain as well, branching F off from H.)

From this new chain, you can see that selecting K prohibits you from selecting T and vice versa.

I'm not sure it's helpful at the outset to make a list of who cannot be together; I would instead approach this question by evaluating the answer choices against the given rules. With this game type (binary grouping, where it's common that all of your rules are conditionals), you'll usually get a question like this that tests your ability to link these conditionals.

The word "must" in a question stem indicates a deduction (and if it's a universal question, like here, it indicates a deduction that holds for the entire game). If something must be true or false in a universal question, that means you have enough information in the given rules to make that concrete determination.

Sometimes these are straightforward deductions, based off a single rule. Imagine a rule in an ordering game that told you A comes before B. One deduction would be that B cannot be first.

A slightly trickier question might require you to connect two or more rules. Imagine that if in addition to knowing A comes before B, you also know B comes before C. If a question asked you who could not be second, you might not immediately see that it's C if you had left the rules separate like this:

A...B
B...C

rather than combining them like this:

A...B...C

This is why it's important to be actively engaged with the rules and possible combinations among rules, especially when they are of they same type or contain the same element.

(Still, other so-called initial deductions are not quite so obvious. Consider PT43.S1.Q5: I doubt most people would immediately deduce that GJ is not a valid block in this game because it relies on the interaction of all of the game rules, rather than just one or two simple rules. This is why some people prefer to leave these universal questions until they've completed the local questions. Completing the local questions allows you to build up an inventory of valid orderings/groupings that you can then use to eliminate answers on universal questions, reducing the amount of testing you have to do.)

So, for this particular question type in this particular game type, it's probably most efficient to start at the first answer choice and evaluate them against your rules until you find an answer choice that violates one. The heavy lifting to be done up front is not generating a list of who can and cannot be together, but instead combining the conditionals rather than leaving them as individual pieces of information. While it is helpful to spend some time familiarizing yourself with the rules before jumping into the questions, it is not usually helpful to start creating mass hypotheticals - you might be doing more work than you actually need to! Let the question stems guide you. I hope some of this is helpful!

[ohthatpatrick]

Fantastic explanation! So well written --- you're going to write some excellent motions for summary judgment.

I'll just quickly add/reinforce two things

- You should ALWAYS turn "can't both be selected" into conditionals. If you otherwise just write an FH and cross it out, you'll be tempted to think they can never be together, but they can both be OUT. Plus, turning them into conditionals allows you to chain them together to other rules.

- If you want, for binary games, there are ways to turn these rules into placeholders in your master diagram.

If they tell me that F and H can't BOTH be IN, then that means that at least one of them is always OUT.

So I could put an F/H+ placeholder in the OUT column.

From rule 2, I could put an N/T+ placeholder in the OUT column.

If you really want to go nuts, you ask yourself these questions:
does F being OUT do anything? no
does H being OUT do anything? no
does T being OUT do anything? no
does N being OUT do anything? yes, it sends K out, which sends H out.

So instead of writing an N/T+ placeholder in the OUT column, you can actually write NKH/T as a placeholder.

If that seems too complicated, do not worry about it. Most people don't do these placeholders and they can still make it through the game just fine.