Conditional Reasoning Diagramming Drill #10

[sim.LSAT]

Hi,

The contrapositive in Q10 is ~kj (j k). This makes sense.

However, why then in Question 3 is the contrapositive not written this way H L M F? Because if in the original statement L's delivery is earlier than H's, then in the contrapositive, L's delivery would be sometime after H's delivery. Also, if Fs delivery is earlier than Ms, then in the contrapositive shouldn't Fs delivery be later/after than M's?

Also....on question 10 it states "this rule produces important inferences at the end points."Are the inferences based on the original diagram? Should our inferences always be based on the original diagram? Would it make a difference if they were based on the contrapositive diagram?

[Adam Tyson]

The reason for the choice to diagram "if L is not before H, then F is not before M" rather than just reversing the order is that a rule like this could show up in a game where some variables could be tied. In a sequence, there are three possible relationships between any two variables: X is before Y, X is after Y, and X and Y are simultaneous. If we knew that this game did not allow for ties, then your approach would be absolutely correct - if L is not before H, then H would have to be before L, and you could just reverse the order when doing the contrapositive. For most linear games, that is exactly what would happen! But some games, especially Advanced Linear games, do allow for two variables to be simultaneous, and you must be prepared to account for that in your diagram. Otherwise, you will fall into traps set by the test makers!

As to those key inferences for #10, you can base them on either the original diagram or the contrapositive, because both diagrams mean exactly the same thing as each other. There is no logical difference between them! That's why the contrapositive of a conditional statement always must be true; it's saying the exact same thing, just in a different way!

[sim.LSAT]

Hi Adam,

Thanks for the reply. That totally makes sense. Since there are 3 possibilities you must account for them all, unless it is specified that there is "no ties." If there are "no ties" then you can simply reverse the order. However in this diagramming drill, the instructions specifically state "with no ties possible." If this is the case, then shouldn't the contrapositive just be the reverse order?

[Adam Tyson]

Yes! If no ties are possible, then "not before" is the same as "after." Good eye, and solid evaluation! So either the diagram we suggested, or the one you proposed, would both be correct in this case. Well done!

[Mastering_LSAT]

Hello,

Could you please walk me through the process of coming up with inferences in #10?

Also, is it correct to diagram the second inference in #10 this way: J2 -> K1 rather than K1 -> J2? Is there any difference? I feel that it may be wrong because I may have switched the sufficient and necessary conditions in these examples.

Please explain. Many thanks!

[Jeremy Press]

Hi Mastering LSAT,

The inferences here come from thinking about what happens at the extreme ends of the line, and thinking about which variable placed on the end point of the line will "trigger" the sufficient condition of the rule.

If J is on 7 (on the end point of the line), then we know for certain that the sufficient condition triggers, because whichever of the other spaces K goes on (1-6), it will be ahead of J. So that means it will have to be in 6, right ahead of J.

The same is true is K is on 1. If K is on 1 (on the end point of the line), then we know for certain that the sufficient condition triggers, because whichever of the other spaces J goes on (2-7), it will be after K. So that means it will have to be in 2, right after K.

Your inference is not necessarily true, because, if J is on 2, K might be on 3 (or 4, or 5, etc.), in which case the sufficient condition of the rule wouldn't "trigger," because J would actually be ahead of K (not after K).

Does that make sense, and answer your question? Hopefully so!

[Tasha68]

Hi Mastering LSAT,

The inferences here come from thinking about what happens at the extreme ends of the line, and thinking about which variable placed on the end point of the line will "trigger" the sufficient condition of the rule.

Hello, I have a question regarding this, so by this logic, shouldn't question #11 be treated the same way too?

The first part of the inference in Question #11, G1 F2 in the extreme left of the line which triggers the Sufficient Condition of the rule.

The second part of the inference, G2 F1 is what is confusing to me.
Shouldn't the inference be F6 G7 (If F cannot be after G, the F must be before G since there are no ties allowed), at the right end of the line, triggering the sufficient condition?
Why must G be 2 and F be 1? Is the way I inferred i.e., F6 G7, also correct?

Please help!

Regards,
Tasha

[Dave Killoran]

Hi Tasha,

Thanks for the message! You're not wrong about the inference, but it is slightly different than #10, and that difference is why I didn't discuss it again in #11. Let's look at the difference:

• In #11, when F is anywhere but 2nd, the relationship is F G. So, it's an immediate and obvious consequence that when F is 6th, G would be 7th. In other words, as the relationship goes to the that endpoint, the expected thing happens. However, when the relationship is at the other endpoint (the first few spaces), the behavior is far different, and so I focused on that relationship.
  
  As for why the G2 F1 relationship works, the easiest way to check that is to place G second. That then means F is not second, which means that F G is in play, and F must be first.
  
  In #10, what made this unusual to me is how when you place J in 7th, you end up placing K in 6th, one space before it. Similarly, placing K in 1 forces J into the spot immediately behind it. While this happens in blocks all the time, you don't often see this in conditional reasoning involving sequencing. It's a bit unexpected for most people (whereas #11 is less so as far as placing F in 6th), hence my decision to make a special note about it.

Please let me know if that helps. Thanks!