Grouping/Linear Combination Setup Practice Drill #4

[tayjbot]

Hi there, In this drill one of the rules is "liu performs on the day immediately before the day nassif performs"

Since there are two "out" spots in this grouping / linear drill, i took that rule to be a conditional statement L L/N .

But according to the answer key the rule creates a block. I mean, since there are two out spots, then l and n don't necessarily have to perform, do they? I guess I just don't understand why this isn't a conditional relationship.

Thanks

[Jon Denning]

Hey tay,

Thanks for the question and welcome to the Forum!

This is a good example of how the test makers will occasionally word things in such a way that you can note not only what the rule says, but also the implications based on how it is written. In this case, when we're told that "L performs on the day immediately before the day N performs," not only would that create an LN block (vertically in this case, since the days are shown up and down), but it also implies that both L and N do, in fact, perform.

If it were the case that they could potentially be in the Out group, the rule would have had to allow for that possibility by saying something like, "If L performs..." Since it states it absolutely, however, we know that those two, L and N, are both in.

I hope that helps!

Jon

[sunnyjoy]

I'm having trouble with the Grouping/Linear Combination Setup Practice Drill #4.
The Answer key says the first rule which is "Liu performs on the day immediately before the day Nassif performs", can be diagrammed as a block, while I thought the rule is conditional, not a block.

I thought since this is a Grouping/Linear game and there is no guarantee that both L and N will be selected, the first rule actually means "If Liu and Nassif is scheduled for performances, Liu performs on the day immediately before the day Nassif performs."
However, since the Answer Key says it is a block, does this mean that under the first rule, only 'both L and N are selected' or 'both L and N are not selected' is possible? Can't L be selected while N is not selected(or vice versa)? Why? I'm so confused... Please help!

[Robert Carroll]

sunny,

The key to this is the way the rule is phrased.

Compare:

"L performs on the day immediately before any day on which N performs"

to

"L performs on the day immediately before the day on which N performs"

The latter implies that there is a day on which N performs, and therefore that N and L both perform. The former is conditional in nature, because it doesn't require that there be any day on which N performs, but if there is, the block with L applies. The difference is "the" in the rule as you copied it, with means there is some day when N performs. It's not a hypothetical day (which makes the rule a conditional), but a definite day when it occurs (making the rule a block).

Robert Carroll

[mabbas]

Immensely confused with this rule setup;

"Fine cannot perform on Saturday unless Hancock perform on Saturday".

I would understand this to be a conditional rule: if H(sa) -> then F(sa)

The answer key elaborates by including E and W stage in the rule, which makes sense. However, it writes the rule as F(sa) -> H(sa). It seems I've misunderstood the necessary and sufficient conditions, but I'm not sure how.

Can you explain how "Fine cannot perform on Saturday unless Hancock perform on Saturday" results in F(sa) -> H(sa)?

Appreciate your help!

[Jeremy Press]

Hi mabbas,

Be careful with your diagramming of "unless" rules! This is something that is addressed in Chapter 3, under "Rule Representation," where we discuss the "Unless Equation."

Go back and check out that discussion, and the rules for dealing with "unless" in conditional statements.

The first step of the Unless Equation is to diagram the part of the rule modified by unless as the necessary condition. Here, Hancock performing on Saturday is modified by unless, so it becomes the necessary condition (on the right side of the arrow), per below:

H(sa)

The second step of the Unless Equation is to negate (i.e., state the logical opposite of) the remaining condition, then diagram it on the sufficient side of the arrow. Here, the remaining condition is "Fine cannot perform on Saturday," so we need to negate that to "Fine can (i.e. does) perform on Saturday" then diagram that on the sufficient side of the arrow, per below:

F(sa) H(sa)

Now we're home free, with the accurate diagram!

The reason this more complex diagramming procedure is required is because of the nature of "unless" statements, which are speaking about exceptions to a normal situation. In this game the normal situation is that Fine cannot perform on Saturday. The exception to that (the necessary circumstance in which Fine CAN perform on Saturday) is when H performs on Saturday. In other words, if the exception (Fine on Saturday) is going to occur, then it MUST be the case that H performs on Saturday. Since the unless statement speaks to that exception (Fine performing on Saturday) our diagram has to reflect that, and it has to reflect that what is necessary for that exception to occur is the "unless" condition (H performing on Saturday). Hence, the Unless Equation above, which gets us to the right logical diagram!

I hope this helps!

[mabbas]

It did. Thank you so much!!!

[jojo0001998]

Hi, I have a question about the inference that N cannot perform on Thursday.

If L doesn't perform at all, couldn't N perform on Thursday? I didn't read the question to mean that L must perform. Instead, I thought it meant that L could perform and if it does, it must be the day before N.

Thanks in advance!

[Adam Tyson]

The rule about L performing is not conditional, jojo0001998, so it's telling us that L MUST perform (and also that N must perform the next day). If the rule had said "If L performs, then N must perform the day after L performs" we would have the situation you described. As it is, that first rule means L and N must always be in the group of 8, and allows us to infer that L is not on Sunday and N is not on Thursday.

Be careful not to treat a rule as conditional when it is presented as a guarantee!

[leslie7]

p. 409, q4, ed. 2020

hi there

For the fifth rule F cannot perform on Sa unless H performs on Sa
I drew it as Fsa-> Fsa E, H sa W (is this ok? or not recommended?)

/Hsaw->/Fsae

Just wondering if under this conditional if it is possible for H to live in Saturday West if F is not on Saturday at all?