Sequencing - Mutually Exclusive Outcomes

[Drackedary]

I am having difficulty understanding the following example on page 381:

R sings at some time before S or at some time after L, but not both.

The LG Bible provides the following diagrams (with S and L on top of each other over the dotted line - I'm not sure how to type that out and have it display properly):

R > S---L

or

S---L > R

I thought the correct diagram would be:

S > R > L

or

L > R > S

My problem here is I am understanding the phrase "but not both" to mean that S and L cannot both, simultaneously, be before or after R, which means R would have to be in the middle. If anyone can help clarify and wrap my head around why the proper diagrams correctly reflect the rule, that will be appreciated. Thanks!

[Nikki Siclunov]

Hi Drackedary,

Thanks for your question.

I'm afraid you misunderstood the implication of the "not both" clause in this case. If I told you, "I'm gonna eat a bagel or a sandwich, but not both" - that means, "I'll have either one, but I won't have both"

Bagel NOT Sandwich

and

Sandwich NOT Bagel.

The same idea is tested with the example on page 381:

R sings at some time before S or at some time after L, but not both.

The first part of the rule requires that one of the following two sequences be always satisfied:

R > S

or

L > R

The second part of the rule ("but not both") warns you that both sequences cannot occur at the same time. Thus:

R > S R > L

and also

L > R S > R

In other words, either both S and L are at some time after R, or else both S and L are at some time before R:

R > S and L

or

S and L > R

Does that make sense? Let me know.

Thanks!

[Drackedary]

Thank-you! I see now that "not both" is referring to the two sequences.

[lawana]

Hi Drackedary,

Thanks for your question.

I'm afraid you misunderstood the implication of the "not both" clause in this case. If I told you, "I'm gonna eat a bagel or a sandwich, but not both" - that means, "I'll have either one, but I won't have both"

Bagel NOT Sandwich

and

Sandwich NOT Bagel.

The same idea is tested with the example on page 381:

R sings at some time before S or at some time after L, but not both.

The first part of the rule requires that one of the following two sequences be always satisfied:

R > S

or

L > R

The second part of the rule ("but not both") warns you that both sequences cannot occur at the same time. Thus:

R > S R > L

and also

L > R S > R

In other words, either both S and L are at some time after R, or else both S and L are at some time before R:

R > S and L

or

S and L > R

Does that make sense? Let me know.

Thanks!

Hi, I understand you explanation better than the book's.
However, your outcome is
(R---S) -----> (R---L)
OR
(L---R)----->(S----R)

which makes R before S and L
or R after S and L.
But the book doesn't have a conditional arrow (--->) to describe this, which makes it confusing to arrive at this outcome.

How do I know I have to do this approach to arrive at the same outcome? the two final outcomes you have there, seems like standard sequencing with the only difference that you have two different outcomes and the phrase "but not both", which makes it mutually exclusive.
In the previous page, where they explain what mutually exclusive is:

R----S
or
R----T
is somehow easier, because the two Rs are on the left side, forming a chain at the end. Also, it has the word either/or.
I just want to make sure on how to properly approach each sequencing conditional rule.

Also, one last question about sequencing, their range level is a little weird.
On previous examples of sequencing, they have TALLER (to left) ----SMALLER (to right)
HEAVIER (to left)----LIGHTER (to right)
which in linear this would have been reverse (lighter to the left and heavier to the right).

however, on the last example of R being before or after S and L; before is on the left and after is on the right.

I'm confused on that , I hope you can help me with these two questions.

Thank you

[Dave Killoran]

Hi Lawana,

Thanks for the questions. If I understand you correctly, you are asking about whether you need to use conditional arrows in representing or arriving at the sequential relationships? You don't—Nikki just chose to use them because that's one way to get to that understanding. But, just as in climbing a mountain there are different paths to the top, the same is the case here: I could have used them as one method of explanation but I chose not to. Of course, when students are uncertain about an idea and ask us about it on the Forum (and the idea under discussion here is a very tough one), that's when we'll often pull out different methods of explanation. It's a standard instructional tool, and the one Nikki chose to use above. Thus, you can choose whichever approach you find the easiest to understand, in exactly the same way a mountain climber can choose the path she likes the most

I'm not sure I follow your question about the ranges, but typically you would use what the game tells you to help determine what the range is, as well as what would be on the left or right. For example, the game might tell you that it's days of the week and you would arrange them Monday-Friday. Or it might be numbered positions 1-7, which you could then number in that order. In a case like tallest or shortest, if they don't tell you the order, you can choose your own (tallest to shortest, or shortest to tallest) and then diagram the rules in relation to that. The diagrams would look like mirror images of each other, but they'd still have the same relationships and the same inferences. So, unless the test specifies it exactly for you, it's a matter of choice.

That's an interesting concept, so let me provide an example. Let's say a game gave you a scenario of five individuals being lined up according to height, but then it didn't tell you if it was shortest to tallest, or tallest to shortest. You'd then have these options:

• Shortest to tallest:
  
  
  1 2 3 4 5
  
  
  
  Tallest to shortest:
  
  1 2 3 4 5

Let's say you were given two rules; let's look at how they'd be reflected differently according to the arrangement you chose:

F is the tallest individual.
G is not the shortest individual.

• Shortest to tallest:
  
  F
  1 2 3 4 5
  G
  
  
  Tallest to shortest:
  
  F
  1 2 3 4 5
  G

As you added rules, your rule representation and inferences would then be reflected in relation to the ordering you chose, and the information would end up being the same in terms of how everything relates. Thus, a person using the first diagram and a person using the second diagram would each end up with the same answers for the questions, despite the fact that their diagrams would be mirror images of each other.

So, in summary: if they tell you how to arrange things or you feel it's obvious (like days of the week), go with that. If it's not obvious and it's more your choice, then represent it either how you feel is best, or how you feel the rules would make it easiest to diagram.

Thanks!

[lawana]

Hi Lawana,

Thanks for the questions. If I understand you correctly, you are asking about whether you need to use conditional arrows in representing or arriving at the sequential relationships? You don't—Nikki just chose to use them because that's one way to get to that understanding. But, just as in climbing a mountain there are different paths to the top, the same is the case here: I could have used them as one method of explanation but I chose not to. Of course, when students are uncertain about an idea and ask us about it on the Forum (and the idea under discussion here is a very tough one), that's when we'll often pull out different methods of explanation. It's a standard instructional tool, and the one Nikki chose to use above. Thus, you can choose whichever approach you find the easiest to understand, in exactly the same way a mountain climber can choose the path she likes the most

I'm not sure I follow your question about the ranges, but typically you would use what the game tells you to help determine what the range is, as well as what would be on the left or right. For example, the game might tell you that it's days of the week and you would arrange them Monday-Friday. Or it might be numbered positions 1-7, which you could then number in that order. In a case like tallest or shortest, if they don't tell you the order, you can choose your own (tallest to shortest, or shortest to tallest) and then diagram the rules in relation to that. The diagrams would look like mirror images of each other, but they'd still have the same relationships and the same inferences. So, unless the test specifies it exactly for you, it's a matter of choice.

That an interesting concept, so let me provide on example. Let's say a game gave you a scenario of five individuals being lined up according to height, but then it didn't tell you if it was shortest to tallest, or tallest to shortest. You'd then have these options:

• Shortest to tallest:
  
  
  1 2 3 4 5
  
  
  
  Tallest to shortest:
  
  1 2 3 4 5

Let's say you were given two rules; let's look at how they'd be reflected differently according to the arrangement you chose:

F is the tallest individual.
G is not the shortest individual.

• Shortest to tallest:
  
  F
  1 2 3 4 5
  G
  
  
  Tallest to shortest:
  
  F
  1 2 3 4 5
  G

As you added rules, your rule representation and inferences would then be reflected in relation to the ordering you chose, and the information would end up being the same in terms of how everything relates. Thus, a person using the first diagram and a person using the second diagram would each end up with the same answers for the questions.

So, in summary: if they tell you how to arrange things or you feel it's obvious (like days of the week), go with that. If it's no obvious and it's more your choice, then represent it either how you feel is best, or how you feel the rules would make it easiest to diagram.

Thanks!

thank you very much, I understand it now. thanks !!!!!!!