Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Basic Linear: Balanced game.

This is the easiest game of the test, and the basic scenario is as follows:

PT24-Dec 1997 LGE-G2-srd1.png

The first rule creates a KJ block, and creates two Not Laws:

PT24-Dec 1997 LGE-G2-srd2.png

The second rule creates a M > P sequence; again, two Not Laws result:

PT24-Dec 1997 LGE-G2-srd3.png

The third rule is conditional:

PT24-Dec 1997 LGE-G2-srd4.png

The fourth rule is also conditional, but the presence of a negative in the sufficient condition makes this rule trickier to interpret than most other conditional rules. The diagram of the rule, and its contrapositive are as follows:

PT24-Dec 1997 LGE-G2-srd5.png

Thus, if P is not second then P is fifth, and if P is not fifth then P is second. Therefore, P must always be second or fifth, which can be shown on our diagram with a split option. P’s placement also affects M via the second rule, and M cannot be fifth or sixth:

PT24-Dec 1997 LGE-G2-srd6.png

The last rule produces a situation where P must perform on either the second day or the fifth day. This rule, in combination with the third rule, produces the following inferences:

PT24-Dec 1997 LGE-G2-srd7.png

The second inference is quite powerful; when L performs third, the entire schedule is determined:
M-P-L-O-N-K-J. This inference is tested in question #7.

[jcough346]

So two questions, first is in the set up of the rules.

Rule 3: Lalitha performs third only if Norton performs fifth.

I drew out:
N5 L3
and the contrapositive as:
L3 N5 (both sides cancelled out)

But after reviewing the right answers this is wrong. What should be happening here?

And my second question concerns the Not Laws, I came to the J and P Not Law in space 1 and the K and M Not Law in space 7. How do you come to the rest of the Not Laws and fixed positioning of the other variables.

[Adam Tyson]

Hey there J, thanks for the question. That third rule with the conditional relationship between L and N is one that causes a lot of folks confusion, and in many ways it is the key rule of this game. The test authors are counting on a few common mistakes being made.

First, take a look at the indicator words in that rule - "only if". That phrase always indicates a Necessary Condition, which goes to the right of the conditional arrow. Don't confuse "only if" with just plain old "if", which denotes a Sufficient Condition that goes to the left of the arrow.

Since "only if" is connected to N in 5th position, that means N5 is the Necessary Condition. The other condition there, L3, is Sufficient, and goes to the left. That's what gets us the diagram in the explanation here, L3 -> N5.

What you have is a Mistaken Reversal of that rule - you got your Sufficient and Necessary conditions backwards. That's going to make the diagram incorrect and the game a whole lot harder, and the authors expect that. Certain questions will play right into that - take a look at Q8, where they ask what could happen if N is 5th. They want you to reject answer C, thinking that N at 5 forces L to 3, but C is actually the correct answer there - the Mistaken Reversal is thinking that when the Necessary occurs the Sufficient must also occur, when it actually doesn't have to.

As to some of the other not laws, you can probably get away without all the P laws - we know P is 2nd or 5th, so putting not laws at 1, 3, 4, etc. is a bit redundant, although still accurate and maybe helpful to you. The interesting ones here are about M - since M is always before P, and P can never be later than 5th, we can infer that M is never later than 4th, giving us those 2 additional not laws at 5 and 6.

Take another look at the conditional rule, and maybe review conditional reasoning from Lesson 2 (and the common indicator words for both Sufficient and Necessary conditions), and it should become clear. Then, tackle the game again with your new and improved skill set and see what happens!

[caroheavey]

Hi, I am working on the lesson three work. The logic game rules state "Lalitha performs third only if Norton performs fifth." How would I diagram an "only if" rule in my logic game diagram?

Thanks.

[Adam Tyson]

Good question, Caroheavey, and one we have handled before (and which causes a ton of confusion, especially for students who are just starting to learn about conditional reasoning). I have moved your post to the thread where we discussed the setup of this game, specifically the rule you are asking about.

Basically, "only if" indicates a Necessary Condition, which goes to the right of your conditional arrow. The other condition in that relationship is the Sufficient Condition, which goes to the left of the arrow. So, "Lalitha performs third only if Norton performs fifth" (emphasis added) means that N fifth is Necessary and L third is Sufficient, like so:

L3 N5

This means that any time you put L third, N has to be fifth, and anytime N is NOT fifth, L cannot be third. Be careful, though! N in fifth position does NOT require that L be in third position! That would be a Mistaken Reversal of the rule. They test that on question 8!

Let us know if you need further elaboration. If conditional reasoning is still not your strong suit, seek it out in whatever materials you are using, whether that is our Logical Reasoning Bible, the Accelerated Course book, or Lesson 2 in the Full Length course books, and practice, practice, practice. Good luck!

[Lulu]

Dear Jon:

I am excited to tell you that, thanks to your advice, today I experienced my first "a-ha" moment when I was completing this logic game.

As I was going through the questions, your voice echoed in my head--"look for the extremes, look for the impossibles"--as if I were watching your circular game video. I understood all five questions thoroughly and answered them correctly!

Even though this game is simple, it felt like I have taken a big step forward! It's encouraging! I gathered all my draft papers with the test paper--Game #4, December 1997 questions 6-10, and put a ribbon on top. I want to remember this moment!

Thank you!

Lulu

[rashidzaman]

Hello

Can you please explain how you arrived at the 2nd inference?

L3->P2-M1K6J7-O4

[Jeremy Press]

Hi Rashid,

Great question, and let's walk through it step by step!

1. The third rule is a conditional rule that means if L is in 3, then N must be in 5. So our first step with L in 3 is to place N in 5.

2. That triggers the contrapositive of the last rule. The contrapositive of the last rule is that if P is not in 5, then P must be in 2. So, since N is in 5, P cannot be in 5, and P must be in 2.

3. With P in 2, the second rule (that P performs at some time after M) forces M to be placed before P, in spot 1.

4. We have to place the KJ block (created by the first rule) somewhere, and now the only place that KJ block can fit is in spots 6 and 7 (with K on 6, and J on 7).

5. At that point, only spot 4 remains open, and we must place our remaining variable (O) there.

I hope this helps!

[morrisonxia]

Why is 2nd rule written as M > P rather than M - P? Does the > mean something else?

[Jeff Wren]

Hi morrisonxia,

The short answer is that it does mean exactly the same thing as M - P and you should diagram this rule as M - P.

The backstory/history is that, many years ago back in the old days, we used to diagram sequencing rules with the greater than sign (>) rather than the dash (-). The reason was that students were already familiar with this symbol from math and understood the difference between "greater than" and "greater than or equal to."

However, because not all sequencing games order from greatest to least, this symbol confused some students for certain games, so we changed the diagramming symbol to a dash (-) for simplicity/clarity.

Unfortunately, some "greater than" signs still appear in older explanations that haven't been updated.