Conditional Sequencing Diagramming Drill #3

[Patr1ck]

Hello,

I have the May 2013 version of the logic games bible isbn: 978-0-9887586-6-7

Page 384 drill number 3: If R is older than T, then neither C nor D is older than F

The FCD relationship is shown in the answer using a normal greater than sign. Shouldn't it be a greater than OR EQUAL TO sign?

It seems C and D could be the same age as F. Is this true, or have I been staring at this book too long??? It bothers me that I can't get something correct that seems so basic...

Regards,
Patrick

[Dave Killoran]

Hi Patrick,

Thanks for the question, and thanks also for using the book

If the game scenario allowed for every possible ordering result (older, younger, same age), you would be correct that it would be a greater-than-or-equal sign. But, for this entire drill, in the directions at the top of page 384 it states, "Assume no ties are possible." Thus, the possibility of equality is eliminated. The reason I did that is two-fold: 1. to make it easier to understand the concept by eliminating some additional possible results and 2. because the games that feature these types of rules are typically Balanced Linear games with 1-to1 relationships, so each variable has to be in a separate spot with no ties. If ties hadn't been specifically eliminated, you would have been on the money, so overall you are showing you have the concept down 100%

Please let me know if that solves the problem for you. Thanks!

[kristinaroz93]

1) On page 386 of the powerscore bible number 3, we are give this conditional statement:
"If R is older than T, then neither C or D is older than F.

And someone on the forum recently asked (which was my question inititally, but luckily I found the explanation on this forum).
"The FCD relationship is shown in the answer using a normal greater than sign. Shouldn't it be a greater than OR EQUAL TO sign?"

Of course normally there should be a greater than or equal sign, but the rules say no ties are possible. So my question is this, can we work out the same problem utilizing the greater than or equal sign. What does the contrapositive look like in that scenario?

Is it this?
R>T---> F≥ C/D
so then:
NOT F≥ C/D---> NOT R>T
Which gives:
C/D≥F----> T>R

Or is this wrong? How do ties change the contrapositive?

2) Also, could someone please diagram out the contrapositive for 3 and 5 with the removal of the negative as was done for 1, I would really like to see it in a visual sense since the book only explains it out in words =)?

Thanks in advance!

[Dave Killoran]

Hi Kristina,

Thanks for the questions!

For #1, ties create subtle effects throughout diagrams, because they introduce a third possibility (the possibility that they are equal/tied). So, you always have to think about the three states (in this case, older/equal/younger), and see what is being allowed or eliminated in each instance. Your initial diagram in #1 is correct (the equal sign gets added to the necessary condition). But, in your contrapositive, the R > T term, when negated, becomes T ≥ R, because the only thing eliminated is R being older than T. The other term is "either C or D, or both, is older than or the same age as F." I think that's what you are saying there, so you were fine with that

For #2, this Forum is not really equipped to handle this type of visualization because the representations aren't easy, but I'll try. This does not include the possibility of ties:

• #3 contrapositive:
  
  
  C > F
  or T > R
  D > F
  
  
  #5 contrapositive:
  
  
  H > F
  or
  J > F H > F
  or
  O > F

Please let me know if that helps. Thanks!

[kristinaroz93]

Dear Dave,

Thank you so much for your response! I really appreciate it. I completely understand part 2 of my question now. However, for part 1, I am not really sure what is meant by "But, in your contrapositive, the R > T term, when negated, becomes T ≥ R, because the only thing eliminated is R being older than T".

Is it this: C/D≥F----> T≥R. And if so, I am not really sure why that is the case since we have not say done that for problem 1 or the others (i.e. turn a greater than sign into a greater than or equal to sign upon finding the contrapositive followed by removal of the negative)! Hope you can clear it up for me here=)

(And yes you have the right idea about what u was saying with c/d !)


Thanks in advance!

[Dave Killoran]

Hi Kristina,

Yes, that is basically the diagram, although I see that I didn't address the sufficient term in my first response, and I should have because the negation of that is different; please see below). My point in discussing the negation of the necessary condition was that "NOT R>T," when negated, translates into "T ≥ R." this occurs because you explicitly added the possibility of ties; if those did not exist, then "NOT R>T," when negated, would translate into "T > R." So, I was simply adjusting for change you made in adding ties.

Why does the negation of the necessary condition work this way? Because there are only three possible relationships between R and T:


R > T
T = R
T > R


So, when you eliminate R > T ("NOT R > T"), that leaves just two possible states:


R > T
T = R
T > R


When combined, those two relationships are diagrammed as T ≥ R. We then put that back into the arrow diagram. So, you had originally stated that:

"If R is older than T, then neither C or D is older than F."

Is it this?
R>T---> F≥ C/D
so then:
NOT F≥ C/D---> NOT R>T
Which gives:
C/D≥F----> T>R

Using that same basic framework and diagramming (mainly the NOT), here's how I'd see it:

• "If R is older than T, then neither C or D is older than F."
  
  Is it this?
  F ≥ C
  R > T and
  F ≥ D
  
  
  so then:
  
  NOT F ≥ C
  or NOT R>T
  NOT F ≥ D
  
  
  Which gives:
  
  C > F
  or T ≥ R
  D > F

Does that help out? I didn't completely follow the rest of your message, so if that doesn't make sense, just let me know. It gets tricky when you change the original parameters of the problem . Thanks!