Conditional Possibilities vs. Certainties Drill

[Sara Gold]

Good afternoon,
I had a lot of trouble with the exercise on pg 2-58, of Lesson 2 homework.
I mostly had trouble differentiating between "Could be True" and "Cannot be True"
Would you have any suggestions or tricks on how to approach this type of drill?
Thank you.

[Dave Killoran]

Hi Sara,

This is a really difficult drill (by design), and it's the kind of drill that really makes you stop and consider how what conditional statements mean, how uncertainty works, and what must, can, and cannot occur under specific statements.

The first thing to realize is that the reasoning being used here is a type that we use every single day. You are actually very familiar with conditional reasoning, but what you aren't familiar with is the kind of cold, clinical usage of conditionality that you see on the LSAT and in this drill. If I changed these drills around to use the names of your friends and family (for example, "if Adam comes to the party then Bjorn comes to the party too (A B); what must, could, and cannot occur if Bjorn comes to the party?" you'd probably feel much more comfortable with this drill

Second, the Could and Cannot parts giving you trouble is pretty normal. But the fact that the Must questions didn't bother you is a good sign—it means that at this point you understand what the immediate consequences are of each conditional statement when you are given a second piece of information. Getting that part down means that understanding the Could and Cannot parts is simply a matter of seeing the rest of the picture. Part of that is simple adjustment. You get asked about what Must occur so frequently in LSAT prep that you get used to that quickly; Could and Cannot questions in this form come up much less, so that unfamiliarity is a big part of the problem.

That said, let's take a look about how to think about a drill like this, by using the first question in #1 as a template. The diagram there is: A B C, and the question posed is what happens when B does not occur ( B )?

I tend to mentally organize it as a set of options for each variable. I know immediately that there are three variables—A, B, and C. But what also exist are their opposites—A, B, and C. So, I'm looking at all this knowing that the different outcomes will revolve around those six basic possibilities.

We know from the question that B does not occur. B appears in the middle of the chain, and so what are the immediate results? Well, the diagram features B, and the question features B, so the condition in the diagram isn't met. That means that for C (which is is "downstream" as C), that anything can happen. Either C could occur or it can not occur; we simply don't know. Hence, on the Could Be True line we'll have both C and C.

Going back to B, we know that is the opposite of B, and so this means that the necessary condition in A B has not occurred, enacting a contrapositive. Consequently, we know that A does not occur ( A ), and thus that is added to the Must Be True line. Well, if A occurs, then the opposite cannot occur, meaning that A cannot occur, and that is added to the Cannot Be True line. At that point, we've looked at all the options for A and C, and that means we're done.

That's the same process I use for each of the problems—examine each variable and it's opposite (such as C and C), and consider the range of what's forced to occur and not occur.

Also, I previously wrote out an explanation for #2 that you might find useful: http://forum.powerscore.com/lsat/viewto ... =28&t=3763

Please let me know if that helps. Thanks!

[Alex3505]

Good evening, I am also having a difficult time with this concept (statement 3 on page 2-65).

The conditional chain is : H or J---> K---> L
I interpret this chain as , if H or J then K and if K then L. So H could occur ( J does not occur) or J occur (H does not occur) to indicate K occurs. If K occurs that indicates that L occurs too.

The question asks me to understand what must occur, what could occur , and what cannot occur if H doesn't occur.
I automatically diagram the contrapositive to better understand the relationship.
Not H and Not J ---> not K---> not L
If H and J do not occur ,K cannot occur which means L does not occur either.

The sufficient condition indicates that the necessary condition must occur, and the necessary condition indicates that the sufficient can occur but does not have to occur. With that being said I am confused on the correct answers in the book.

If "Not K" is in the middle of the chain does it not act as a sufficient and necessary condition?
Not H and not J ---> not K
Not K---> not L

So if H does not occur, then what must be true is K does not occur and because K does not occur L cannot either.
The correct answer is that nothing was written under Must Be True or Cannot Be True , only Could Be True.

I'm also having a hard time with " If K does not occur" what must be true, cannot be true, or could be true.

Sorry for the long question/ explanation.
Thank You in advance.
-Alex

[Luke Haqq]

Hi Alex!

First, I think the problem might lie in the way you diagrammed the contrapositive:

I automatically diagram the contrapositive to better understand the relationship.
Not H and Not J ---> not K---> not L

For contrapositives, you flip and negate the sufficient and necessary conditions. For example,

A B

becomes:

not B not A

And as you correctly noted, you change the "and" to "or" (or vice versa) if those words are used. Using these rules, the contrapositive instead should be:

Not L Not K Not H and Not J

Second, you write:

I interpret this chain as , if H or J then K and if K then L. So H could occur ( J does not occur) or J occur (H does not occur) to indicate K occurs. If K occurs that indicates that L occurs too

When you see "H or J K," that doesn't mean that you're definitely going to have H or J. That is, if H occurs, this doesn't tell you anything about whether J occurs. And if J occurs, this doesn't tell you whether or not H occurs. Rather, you know from that diagram that if one of those occurred (which would happen if both of them occurred), then you know K occurs. And the contrapositive would tell you that if K does not occur, then H does not occur and J does not occur.

With those explanations, you should be able to tackle the problems in #3. If H does not occur, we don't have anything from the contrapositive or original statement telling us what must/could/could not be true. "Not H" would need to be a sufficient condition in one of the diagrams (it would need to be on the left side of the arrow. And in the contrapositive we do have "Not K" as a sufficient condition--as mentioned, we know that if K does not occur, then H did not occur and J did not occur.

Hope that helps!

[acp25]

Hi,

I'm having a difficult time understanding #4 on Page 2-66 - If O occurs, what could be true.
The statement is:
NOT N O P or Q

I broke it down as:
NOT N O
N NOT O

O P or Q
NOT P and NOT Q NOT O

NOT N P or Q
NOT P and NOT Q N

Am I wrong in my interpretation?
Why are the answers the way they are?

Thanks in advance!
Amy

[AthenaDalton]

Hi Amy,

Your diagrams were partially correct!

You diagrammed the contrapositive of this relationship perfectly:

Original: O P or Q
Contrapositive: P and Q O

From this diagram we can conclude that if O occurs, P or Q or both must occur. We can also conclude that it cannot be true that neither P nor Q occur.

Things went a little sideways in diagramming the relationship between N and O. Here's how that one works:

Original: N O
Contrapositive: O N

It looks like you negated the terms, but forgot to place O and N on opposite sides of the diagram. The takeaway from this relationship is that if O doesn't occur, N has to occur. But there's still the possibility that O occurs and N occur at the same time! That's why the "could be true" list includes both the possibilities of N occurring and not occurring.

I hope this helps clarify things for you. Good luck studying!

Athena