Conditional Indicators

[DlarehAtsok]

In the book it says that there are certain indicators for sufficient and necessary conditions. I was wondering whether I can find both of the them in a sentence, e.g. "You are required an ID, only if you want to drink alcohol". Is there any way to determine that only if is a stronger indicator than required for a necessary clause, or this sentence does not work logically and the true form would have to be "You are required an ID, if and only if you want to drink alcohol".

[Nikki Siclunov]

Hi DlarehAtsok,

Thanks for your question! Yes, it is entirely possible to find multiple sufficient and/or necessary conditions in a sentence, because a single sentence can convey multiple conditional relationships. This is infrequent, but it happens. Let's take a look at the example you provide:

You are required an ID, only if you want to drink alcohol

How you interpret this sentence depends on context, because syntactically the statement needs some work Say, you're going to a bar and they tell you that "you need an ID to drink alcohol," then the conditional relationship would look like this:

Drink alcohol ID required

On the other hand, if they say: "ID required, but only if you want to drink alcohol," then the ID requirement is itself subject to a necessary condition, namely, buying alcohol. In this instance, the conditional relationship would look like this:

ID required Drink alcohol

This is because in the second example, unlike in the first, the ID requirement is limited to drinking alcohol: if you want to get soda, for example, you won't need to show your ID.

Now, let's take a look at another, more complicated scenario. Let's say you go to a club and the doorman tells you:

"Buddy, you need to wait to get in, unless you have a special pass."

In this case, we have two necessary condition indicators: waiting is clearly a necessary condition for getting in (Get In Wait), unless you already have a special pass (in which case, presumably, you wouldn't need to wait). So, the conditional relationship between waiting to get in and getting in is modified by a necessary condition indicator (unless). Using the Unless Equation, we can diagram this sentence as follows:

NOT (Get In Wait) Special Pass

"Nested" conditionals are complicated for the purposes of the LSAT, so let's think about what this means. What does it take to get in? You can either wait or have a special pass! Since you only need to satisfy one of these two conditions to get your table, we can re-write this statement as follows:

Get In Wait OR Special Pass

Does this make sense? Let me know.

Thanks!

[LSAT2018]

NOT (Get In Wait) Special Pass
I was reading through the last part of your post and would like to request additional explanation for this. If the unless creates the NOT part, would it be NOT get in and NOT wait?


Thanks in advance!

[Dave Killoran]

NOT (Get In Wait) Special Pass
I was reading through the last part of your post and would like to request additional explanation for this. If the unless creates the NOT part, would it be NOT get in and NOT wait?


Thanks in advance!

Hi LSAT, that unfortunately won't work. What your example does is negate each individual part, when the requirement here is to simply negate the existing relationship in the condition. Here's an analogy:


To get into Harvard, you must be intelligent (H I)


If I say that statement isn't true, it's basically saying NOT (H I), just that it's not true that to get into Harvard you must be intelligent. Does that then mean if you are not at Harvard then you're not intelligent? No, that goes way too far, but that's what Not H Not I would be saying

What Nikki was attempting to get across was the broad idea that the entire relationship is negated, hence he chose to simply negate the entire condition and not go further. As a reference, the specific negation of that condition is "to get into Harvard you don't necessarily need to be intelligent."

Please let me know if that helps. Thanks!

[LSAT2018]

If I say that statement isn't true, it's basically saying NOT (H I), just that it's not true that to get into Harvard you must be intelligent. Does that then mean if you are not at Harvard then you're not intelligent? No, that goes way too far, but that's what Not H Not I would be saying

I initially thought nested conditionals were like multiplication and percentages so these nested conditionals are confusing me (HELP). So how would you actually diagram the it's not true that to get into Harvard you must be intelligent part (something like it is not true that A → B)? Would it be more like weakening the necessary part, ie. to get into Harvard you do not need to be intelligent in other words, A → NOT B?

In this case, we have two necessary condition indicators: waiting is clearly a necessary condition for getting in (Get In Wait), unless you already have a special pass (in which case, presumably, you wouldn't need to wait). So, the conditional relationship between waiting to get in and getting in is modified by a necessary condition indicator (unless). Using the Unless Equation, we can diagram this sentence as follows:

NOT (Get In Wait) Special Pass

"Nested" conditionals are complicated for the purposes of the LSAT, so let's think about what this means. What does it take to get in? You can either wait or have a special pass! Since you only need to satisfy one of these two conditions to get your table, we can re-write this statement as follows:

Get In Wait OR Special Pass

So back to this conditional statement! How does this change to Wait OR Special Pass? I don't see how the sufficient could become the necessary condition like this.

[Adam Tyson]

Nested conditionals ARE confusing, LSAT-2018! First, let's look at the negation of the conditional claim: Nikki's example was NOT (Get In Wait). What that is saying in plain English is "it's not true that to get in you have to wait". In other words, it is DENYING that there is such a conditional relationship. That's not the same as saying Get In Wait - that would mean that if you get in then you absolutely did NOT wait, when all we really wanted to say was that waiting wasn't necessary. Your illustration makes this error - you went from NOT (A B) (which means A is not sufficient for B; A occurring tells you nothing about whether B occurs) to A B (which means A is sufficient for B not occurring). Important difference!

In short, denying that a conditional relationship exists is not the same as claiming that the opposite relationship does exist.

Back to Nikki's example, now. His original claim was you have to wait to get in unless you have a special pass. Breaking that into its component parts, there is a necessary condition introduced by the word "unless", and that necessary condition is having a pass. The sufficient condition, following the Unless Equation, is the negation of the other condition in the relationship. In this case, that other condition was, itself, a conditional claim: you have to wait to get it, or Get In Wait. The negation of that claim is "it's not true that you have to wait to get in" or "NOT (Get In Wait). Putting that all together, we get the nested approach:

NOT (Get In Wait) Special Pass

The contrapositive would be:

Special Pass (Get In Wait)

Now, how did we get to a necessary condition of Wait OR Special Pass? It might help to take a holistic approach to the meaning of all these rules. What would we know if you get in? Well, either there is that conditional of having to wait, or else, if that rule does NOT apply, then you have to have had a special pass. Either waiting is required or, if it isn't (triggering the first nested conditional claim above), then you have to have that Pass. Getting in requires at least one of the two, waiting of having a pass. Makes sense in the real world, and it also mechanically follows the rules. We could, if we like, redo the diagram as Nikki did:

Get In Wait OR Special Pass

Let us know if that doesn't clear it up!

[ryanshort8883]

Hello,

Is all you're doing to get to

Get In Wait OR Special Pass

is just using the fact that

A B is logically equivalent to NOT(A) OR B and then rearranging terms and using rules to get back to a conditional statement?

I think I figured it out, just wanted to make sure I'm correctly using the rules.

Regarding Adam's post, what I did was:

NOT(Get In Wait) Special Pass is logically equivalent to [(Get In AND NOT(Wait))] Special Pass

then taking the contrapositive gives NOT(Special Pass) [NOT(Get In) OR Wait]

which is logically equivalent to NOT(Special Pass) (Get In Wait)

I believe that's what Adam was doing and just didn't show all of the derivation, is that correct?

Thank you!

[Adam Tyson]

You got it, ryanshort8883! There's more than one way to deal with a nested conditional, and yours works just fine! Well done.