Not Laws HQR example

[ashley]

I’m reading the logic games bible, but I can’t seem to understand the not laws. How do you get all the letters under all the slots, the book does not explain how all the letters go there. For example, on page 23 at the bottom (H>Q>R) how did you come up with the letters under the slot? Thanks!

[Dave Killoran]

Hi Ashley,

Thanks for the message, I’m happy to help you out with your question. First, go back to page 16 and re-read the Not Laws section--I think that will help provide a good background on what I say below.

Basically, a Not Law simply shows something that can never happen. So, with the H > Q > R example on page 23, consider where H can go. Can H go last? No, because then there wouldn’t be room for Q and R to go behind H. So, we put a not-H under the last slot, slot 6. Could H go in slot 5? No, because that wouldn’t leave enough room for both Q and R to fit. So, we put a not-H under slot 5.

The simple way of doing this is to consider each letter and where it can’t go:

• H can’t go in the last two spaces because there are two variables behind it.
  
  Q can’t go in the last space because R is behind it, and Q can’t go in the first space because H is ahead of it.
  
  R can’t go in the first two spaces because there are two variables ahead of it.

Does that help? Please let me know.

Thanks!

[ashley]

Thanks!

Yes, that helps a lot

[Logicstuff]

First, the information provided for the last post was extremely helpful... but I am still struggling with "not laws" and it is preventing me from proceeding. Page 34 # 3 (amongst others) I cannot properly place the not laws. a) what determines what slot & level within the slot I place the variables? b) how do I determine all variables that need to be included?

The "not laws" I came up with were ...

1
E slash
C slash

2
C slash

5
D slash

6
D slash
E slash

The book lists way more not laws and I cannot figure out why, as I in my best efforts have determined and listed what variables cannot go where.

Any help would be most appreciated as not grasping this one concept is resulting in many missed answers.

Thanks in advance.

[Dave Killoran]

Hey Logic,

Thanks for the message. Here's a general tip for dealing with Not Laws that you can't see at first: try placing the variable in question into that slot, and see what happens as a result. When a variable can't be in a particular space, when you try to put it there you will find that you can't create a workable solution to the problem. That's a great way to reverse engineer the issue, and find the root of what causes the Not Law.

Now, turning to the problem you reference, the Not Laws in this problem have everything to do with the massive block created by the condition in the question. As you can see in the answer key, we have a block that looks like this:

D E __ __ C

Let's consider for a moment where we can place that block. It's pretty big--from D to E consumes 5 spaces--so there aren't actually many places that block can go. And, in fact, it is limited to just to placements: slots 1-5 or slots 2-6. So, consider how that affects a variable such as C. C can only be placed in slots 5 or 6, so C can't be placed in slots 1-4, and C Not Laws appear on slots 1-4. There are similar limitations on D and E, and those limitations create the rest of the Not Laws.

Also, the "level" placement doesn't have a material affect on the meaning of the Not Law; that is, all Not Laws are equal, whether it is the first one listed or the last one listed. How they end up being placed is a result of your "starting point" of analysis. For example, if I start at the "end" of the block and examine C first, C Not Laws will appear first on the list. If I start at the "front," D Not Laws would be written in first, etc.

That's a start, so take a look at the problem again and let me know if the above info helps you solve the problem. If not, let me know and we'll tackle it again. Thanks!

[Logicstuff]

Thank you again! I was able to follow your instructions, but I still was not able to get the correct answer for the not laws.

I was able to determine correctly my original not laws through using "sequencing" & I came up with D>E D>C E>C , reversing them and listing the not laws on diagram.

Are you able to determine why this strategy is not resulting in all of the not laws that the book lists?

Again any feedback would be much appreciated.

[Dave Killoran]

If I understand your post correctly, what is occurring is that you are turning a fixed block formation into a sequence. This is a problem because while a block has fixed positioning (for example, in the question we are discussing, E is exactly one space after D), in sequences the variables move around (E might be one space after D, or two spaces after D, or three spaces after D, etc). So, you aren't accounting for the fixed positioning of the block, and this is causing you to ignore the two empty spaces in the block. For example, consider E. E is after D, which is true in both the block and your sequential relationship. But how does E relate to C? In the block, there are exactly two spaces between E and C. But in your sequence, that isn't represented, and that is why you keep missing the Not Laws for the problem.

The broad point to draw is that you have to look at the nature of the rules: some are sequential, some are fixed, and some are of other types. But each acts differently, and thus the implications of each are different, and that is what the book is trying to teach you in these drills.

Please let me know if that helps. Thanks!

[Logicstuff]

I had to take my time and work through this but I finally understand! Thanks so much for all of the information, its much appreciated!

[tqcells]

Hey Logic,

Thanks for the message. Here's a general tip for dealing with Not Laws that you can't see at first: try placing the variable in question into that slot, and see what happens as a result. When a variable can't be in a particular space, when you try to put it there you will find that you can't create a workable solution to the problem. That's a great way to reverse engineer the issue, and find the root of what causes the Not Law.

Now, turning to the problem you reference, the Not Laws in this problem have everything to do with the massive block created by the condition in the question. As you can see in the answer key, we have a block that looks like this:

D E __ __ C

Let's consider for a moment where we can place that block. It's pretty big--from D to E consumes 5 spaces--so there aren't actually many places that block can go. And, in fact, it is limited to just to placements: slots 1-5 or slots 2-6. So, consider how that affects a variable such as C. C can only be placed in slots 5 or 6, so C can't be placed in slots 1-4, and C Not Laws appear on slots 1-4. There are similar limitations on D and E, and those limitations create the rest of the Not Laws.

Also, the "level" placement doesn't have a material affect on the meaning of the Not Law; that is, all Not Laws are equal, whether it is the first one listed or the last one listed. How they end up being placed is a result of your "starting point" of analysis. For example, if I start at the "end" of the block and examine C first, C Not Laws will appear first on the list. If I start at the "front," D Not Laws would be written in first, etc.

That's a start, so take a look at the problem again and let me know if the above info helps you solve the problem. If not, let me know and we'll tackle it again. Thanks!

Hello,

I have been looking at this problem last few days and can't figure it out. I just don't see where rest of the not laws are coming from.

[Francis O'Rourke]

Hi Tq,

If you are having trouble with these not laws, I'd recommend trying to limiting your focus to one of the variables at a time. Let's start with the variable D. If you understood what Dave wrote above about D, you can skip to the next part. If not, let's look at the rule again.

C must sit 4 chairs behind D

According to this rule, if we diagram 6 spaces, left to right, with left being the front and right being the back, as is shown on this page, D cannot go in space 6.

As Dave said above, if you aren't sure why, then try to place the variable in that space. When we place D in space 6, we no longer have any extra space for C to go. Repeat this for spaces 5, 4, and 3. Every time you place D into one of these spaces, there is no longer room left for C on the diagram, which informs us that D cannot be placed in these positions, 3, 4, 5, and 6.

Since we now see that D cannot go into these places, we want to mark that somehow to remember it when we work through the questions. This is what the Not Laws, explained earlier in the book, are fantastic for. Every time you see that a variable cannot go into a particular space, you can mark it below the space with a slash through it. This is how we get [Not D] under spaces 3 - 6. Try the same thing with C now.

C must be placed 4 spaces to the right (behind) D, so can it be placed in space 1? Once you figure out the spaces it cannot go (because there isn't enough room left for D), mark it with a Not Law underneath the space.

Try this again for the variable E. At the end, you should come up with something very similar to the diagram in the book.

Let me know if you have any further questions here