How to draw this statement? Forum

[ioannisk]

how would you draw "a bill that most people favor will be passed promptly into law in a well-functioning democracy if the bill does not violate anyone's basic human rights."

is it: Well-Functioning Democracy------>bill does not violate anyone's basic human rights -----> (bill that most people favor --->passsed promptly into law)

would it's reversal be

~(bill that most people favor --->passsed promptly into law)) --------->bill does violate basic human rights ------> Well-functioning democracy


it's so confusing :/

[myoung7189]

how would you draw "a bill that most people favor will be passed promptly into law in a well-functioning democracy if the bill does not violate anyone's basic human rights."

is it: Well-Functioning Democracy------>bill does not violate anyone's basic human rights -----> (bill that most people favor --->passsed promptly into law)

would it's reversal be

~(bill that most people favor --->passsed promptly into law)) --------->bill does violate basic human rights ------> Well-functioning democracy


it's so confusing :/

Definitely is a tough one.. when diagramming conditionals I focus on words that indicate necessity or sufficiency. The only word I see indicating one or the other is if so:

If the bill does not violate anyone's basic human rights ------> a bill that most people favor will be passed promptly into law in a well-functioning democracy.

No other ifs, depends, relies, unless in there so don't make it harder than it needs to be.

[Jeffort]

You're talking about AC (E) from PT70 LR1 #23

Diagram:

If Bill doesn't violate basic rights AND Most people Favor Bill AND a well functioning democracy ---> then Bill will pass promptly

This conditional statement works to justify the conclusion that the country doesn't have a well functioning democracy via application of its contrapositive triggered by a fact we're given in the premises of the argument.

According to the facts in the stimulus the bill will not be passed for many years (meaning ~pass promptly), thereby negating the necessary condition of the conditional relationship AC (E) gives you, triggering the necessary conditions of the contrapositive.

~Bill pass promptly ---> ~bill doesn't violate basic rights OR ~most favor bill OR ~well functioning democracy.

Since a premise tells us the bill will not pass promptly, at least one of the following three necessary conditions must be true due to the OR connectors. The premises in the argument already tell us that the bill doesn't violate basic human rights and that most people favor the bill, establishing that two of the three necessary conditions are false, logically establishing that the only remaining option must be true, there isn't a well functioning democracy in that country.

It's a very tricky/complex way to use application of the contrapositive of a compound conditional statement to support the conclusion since you have to notice that facts from the premises in the stimulus establish that two of the three necessary OR conditions of the contrapositive are already established as false, ruling out two of the three OR options, thereby isolating and establishing that there must not be a well functioning democracy. To make it extra complex, you have to properly identify that AC (E) gives you three sufficient conditions with AND connectors, and realize that the contrapositive turns those into ORs and that you have facts in the stimulus to trigger the sufficient condition of the contrapositive of (E) and rule out two of the three necessary condition options of the contrapositive to prove the only remaining option must be true.

Basically there is a chain of multiple logical steps involved in analyzing (E) to fully see how it gives you a complex conditional that is triggered in several ways by the facts given in the premises of the argument to lead to establishing the conclusion with conditional logical.

Does this help clear up confusion with the question and how (E) is correct?
Which trap answer did you go with if you got it wrong?

[ioannisk]

You're talking about AC (E) from PT70 LR1 #23

Diagram:

If Bill doesn't violate basic rights AND Most people Favor Bill AND a well functioning democracy ---> then Bill will pass promptly

This conditional statement works to justify the conclusion that the country doesn't have a well functioning democracy via application of its contrapositive triggered by a fact we're given in the premises of the argument.

According to the facts in the stimulus the bill will not be passed for many years (meaning ~pass promptly), thereby negating the necessary condition of the conditional relationship AC (E) gives you, triggering the necessary conditions of the contrapositive.

~Bill pass promptly ---> ~bill doesn't violate basic rights OR ~most favor bill OR ~well functioning democracy.

Since a premise tells us the bill will not pass promptly, at least one of the following three necessary conditions must be true due to the OR connectors. The premises in the argument already tell us that the bill doesn't violate basic human rights and that most people favor the bill, establishing that two of the three necessary conditions are false, logically establishing that the only remaining option must be true, there isn't a well functioning democracy in that country.

It's a very tricky/complex way to use application of the contrapositive of a compound conditional statement to support the conclusion since you have to notice that facts from the premises in the stimulus establish that two of the three necessary OR conditions of the contrapositive are already established as false, ruling out two of the three OR options, thereby isolating and establishing that there must not be a well functioning democracy. To make it extra complex, you have to properly identify that AC (E) gives you three sufficient conditions with AND connectors, and realize that the contrapositive turns those into ORs and that you have facts in the stimulus to trigger the sufficient condition of the contrapositive of (E) and rule out two of the three necessary condition options of the contrapositive to prove the only remaining option must be true.

Basically there is a chain of multiple logical steps involved in analyzing (E) to fully see how it gives you a complex conditional that is triggered in several ways by the facts given in the premises of the argument to lead to establishing the conclusion with conditional logical.

Does this help clear up confusion with the question and how (E) is correct?
Which trap answer did you go with if you got it wrong?

thank you so much! I was able to disregard other answer choices which lead me to E, which felt right, but I had difficulty diagramming it.


Why is it If Bill doesn't violate basic rights AND Most people Favor Bill AND a well functioning democracy ---> then Bill will pass promptly


It sounds like the passage is qualifying a conditional statement "most favor bill ----> bill pass promptly" with another conditional "if bill doesn't violate basic rights" and with a further one "in a well fucntioning democracy"

How am I wrong?

How does the wording lead you to making all the conditions sufficient, together, for "bill will pass promptly"

Should I just lump all the sufficient conditions all together when I see passages like this?

[Christine (MLSAT)]

I think the reason it may feel weird to you to string the sufficient clauses together is because in real life we tend to 'tier' these kind of triggers.

Imagine that you're 10, and there are a series of rules that only apply at your very proper Grandma's house. A few of those rules are "dinner rules" that Grandma doesn't worry about during breakfast, or casual lunch. Of those dinner rules, there are 3 that apply specifically to when soup is served. Only one of those rules applies to clam chowder. Whew!

In real life, we categorize these rules in a mental outline format. But logically speaking, if we hit each one of those goalposts, then that final clam chowder rule has to be in play. So:

If [at Grandma's house] AND [dinnertime] AND [soup is served] AND [clam chowder] --> [weird etiquette thing]

Now, if it was a given in the question being asked that we were obviously at Grandma's house the whole time (or perhaps the question was specifically about 'things that happen at Grandma's house), then we could simplify our lives by removing that first sufficient trigger and just expressing the rule as:

If [dinnertime] and [soup is served] and [clam chowder] --> [weird etiquette thing]

This approach is particularly useful on PT62-S4-Q18. The entire question plays out the conditionals that are true if sentient beings outside our solar system exist. It makes sorting everything a great deal easier if you just leave that as an overarching condition that you're working within.

On the 'well-functioning democracy' question, though, we don't have that luxury.

[ioannisk]

I still don't understand

[Christine (MLSAT)]

I still don't understand

Hmm, I think I wasn't very clear.

So, imagine Grandma has a rule that clam chowder must be eaten with a golden spoon. But this rule only applies when you are at Grandma's house. So, it's not actually accurate to just say "if clam chowder, then golden spoon". That rule doesn't apply all the time.

So, when DO you have to use a golden spoon? What situation would guarantee that you will use a golden spoon?

[ioannisk]

Grandmas house. But it still strikes me as grandmas house ~~~~> rule exists (clam chowder~~~~~>spoon). If rule doesn't exist then you know for a fact that you'r not at grandmas house. Am i retarded?!? I don't get why the correct answer is making it grandma house and clam chowder ~~~~> spoon

[ioannisk]

Grandmas house. But it still strikes me as grandmas house ~~~~> rule exists (clam chowder~~~~~>spoon). If rule doesn't exist then you know for a fact that you'r not at grandmas house. Am i retarded?!? I don't get why the correct answer is making it grandma house and clam chowder ~~~~> spoon

Now I realize if you don't have to use a spoon, then you can know your not a grandmas house or you don't have clam chowder. My inference can't conclude that. Hmmm ok I think it's clicking now

[Christine (MLSAT)]

Grandmas house. But it still strikes me as grandmas house ~~~~> rule exists (clam chowder~~~~~>spoon). If rule doesn't exist then you know for a fact that you'r not at grandmas house. Am i retarded?!? I don't get why the correct answer is making it grandma house and clam chowder ~~~~> spoon

Now I realize if you don't have to use a spoon, then you can know your not a grandmas house or you don't have clam chowder. My inference can't conclude that. Hmmm ok I think it's clicking now

You're getting there!!

Okay, so *you're right* that if you're at Grandma's house, then the rule exists - that's the nesting version. It's totally correct. It's just ALSO possible to write the rule the other way.

Think about it: if I told you that I was at Grandma's house, and then separately I mentioned that I was eating clam chowder, those two pieces of information would be enough to conclude that I have to be using a golden spoon. It doesn't really matter which one of those pieces triggers a rule about the other piece. I could just as easily say that when you are eating clam chowder, there are rules - one of those rules is that "If you are at Grandma's house --> use a golden spoon!". We might be inclined to write this:

clam chowder --> rule exists (grandma's house --> golden spoon)

Even though the nesting would be reversed, the practical and logical outcome is identical. Two things together trigger the requirement of the golden spoon: 1) clam chowder and 2) grandma's house.

And you're right about what happens if we AREN'T using a golden spoon. If we aren't using a golden spoon one explanation is that the rule exists (we're at Grandma's), but we aren't eating clam chowder. The other explanation is that the rule doesn't exist (and therefore we aren't at grandma's house). We can actually get to both of these possibilities using the nested format of the if/thens, but it's difficult to wrap the mind around. It's simply far easier to see the exact same implications if we simply turn the nested format into a compound conditional.

Thoughts?

[ioannisk]

Yup! I think i understand now!


I just hope to run into more problems like this so i can get familiar

[Jeffort]

Maybe it would have been clearer if I wrote it out as a nested conditional within another conditional. I didn't because those usually are more confusing for students, especially when it comes to properly applying the contrapositive.

The nested version:

Well functioning democracy --> (Bill doesn't violate basic rights AND Most people Favor Bill ---> Bill will pass promptly)

Contrapositive:
~(Bill doesn't violate basic rights AND Most people Favor Bill ---> Bill will pass promptly) --> ~Well functioning democracy

To apply that properly it's essential to understand what the negation of a conditional statement is/means to know when you factually have satisfied the sufficient condition of our above contrapositive:
~(Bill doesn't violate basic rights AND Most people Favor Bill ---> Bill will pass promptly)

For many people it's conceptually more difficult/confusing to properly understand, think through and apply the contrapositive with nested conditionals since you have to understand what the proper logical negation/opposite of a conditional statement is/means. Negating conditional statements properly can be very confusing, students get confused about it frequently when they learn about the negation technique for solving necessary assumption questions and try to do it with answer choices that present conditional statements.

Either way of representing them is valid, it's just more confusing to work with nested conditionals. Putting everything together properly into a single compound conditional instead of nested ones is easier to work with and apply without confusion.

[ioannisk]

I think the reason it may feel weird to you to string the sufficient clauses together is because in real life we tend to 'tier' these kind of triggers.

Imagine that you're 10, and there are a series of rules that only apply at your very proper Grandma's house. A few of those rules are "dinner rules" that Grandma doesn't worry about during breakfast, or casual lunch. Of those dinner rules, there are 3 that apply specifically to when soup is served. Only one of those rules applies to clam chowder. Whew!

In real life, we categorize these rules in a mental outline format. But logically speaking, if we hit each one of those goalposts, then that final clam chowder rule has to be in play. So:

If [at Grandma's house] AND [dinnertime] AND [soup is served] AND [clam chowder] --> [weird etiquette thing]

Now, if it was a given in the question being asked that we were obviously at Grandma's house the whole time (or perhaps the question was specifically about 'things that happen at Grandma's house), then we could simplify our lives by removing that first sufficient trigger and just expressing the rule as:

If [dinnertime] and [soup is served] and [clam chowder] --> [weird etiquette thing]

This approach is particularly useful on PT62-S4-Q18. The entire question plays out the conditionals that are true if sentient beings outside our solar system exist. It makes sorting everything a great deal easier if you just leave that as an overarching condition that you're working within.

On the 'well-functioning democracy' question, though, we don't have that luxury.

Hi, I went through PT 62 The other day and the exact question you mentioned (PT62-S4-Q18) made me think of this question.

I have a few questions:

1. Why is the first "if" statement in the passage (if there are sentient beings on planets outside our solar system) is pretty much disregarded in finding the correct answer?

2. D states: "If sentient being on another planet cannot communciate with us, then the only way to detect its existence is by sending a spacecraft to its planet" Why is this question approached as an if then statement, where it is drawn as:

If sentient being on another planet cannot communciate with us------> (if to detect its existence, then you must by sending a spacecraft to its planet)

and not the way you guys suggested for the question I asked about pt 70 in the orignial post?

[ioannisk]

Maybe it would have been clearer if I wrote it out as a nested conditional within another conditional. I didn't because those usually are more confusing for students, especially when it comes to properly applying the contrapositive.

The nested version:

Well functioning democracy --> (Bill doesn't violate basic rights AND Most people Favor Bill ---> Bill will pass promptly)

Contrapositive:
~(Bill doesn't violate basic rights AND Most people Favor Bill ---> Bill will pass promptly) --> ~Well functioning democracy

To apply that properly it's essential to understand what the negation of a conditional statement is/means to know when you factually have satisfied the sufficient condition of our above contrapositive:
~(Bill doesn't violate basic rights AND Most people Favor Bill ---> Bill will pass promptly)

For many people it's conceptually more difficult/confusing to properly understand, think through and apply the contrapositive with nested conditionals since you have to understand what the proper logical negation/opposite of a conditional statement is/means. Negating conditional statements properly can be very confusing, students get confused about it frequently when they learn about the negation technique for solving necessary assumption questions and try to do it with answer choices that present conditional statements.

Either way of representing them is valid, it's just more confusing to work with nested conditionals. Putting everything together properly into a single compound conditional instead of nested ones is easier to work with and apply without confusion.

Why do you infer this statement "Bill doesn't violate basic rights AND Most people Favor Bill ---> Bill will pass promptly"

and not

"if bill doesn't violate basic rights ----> (Most people favor bill ---->bill will pass promptly)"

[Jeffort]

Maybe it would have been clearer if I wrote it out as a nested conditional within another conditional. I didn't because those usually are more confusing for students, especially when it comes to properly applying the contrapositive.

The nested version:

Well functioning democracy --> (Bill doesn't violate basic rights AND Most people Favor Bill ---> Bill will pass promptly)

Contrapositive:
~(Bill doesn't violate basic rights AND Most people Favor Bill ---> Bill will pass promptly) --> ~Well functioning democracy

To apply that properly it's essential to understand what the negation of a conditional statement is/means to know when you factually have satisfied the sufficient condition of our above contrapositive:
~(Bill doesn't violate basic rights AND Most people Favor Bill ---> Bill will pass promptly)

For many people it's conceptually more difficult/confusing to properly understand, think through and apply the contrapositive with nested conditionals since you have to understand what the proper logical negation/opposite of a conditional statement is/means. Negating conditional statements properly can be very confusing, students get confused about it frequently when they learn about the negation technique for solving necessary assumption questions and try to do it with answer choices that present conditional statements.

Either way of representing them is valid, it's just more confusing to work with nested conditionals. Putting everything together properly into a single compound conditional instead of nested ones is easier to work with and apply without confusion.

Why do you infer this statement "Bill doesn't violate basic rights AND Most people Favor Bill ---> Bill will pass promptly"

and not

"if bill doesn't violate basic rights ----> (Most people favor bill ---->bill will pass promptly)"

Because if you do it that way, figuring out how to include the 'well functioning democracy' condition properly can get confusing since you'll have to make it so you end up having two layers of nested condition statements, with one conditional nested inside another conditional that is already nested in another conditional to end up with:

If well functioning democracy --> (if bill doesn't violate basic rights ----> (Most people favor bill ---->bill will pass promptly))

Properly understanding and applying that double nested representation of what (E) says with two layers of nested conditionals is confusing and overly complicates things in ways that gives more opportunities to mess things up/get confused.

Also, AC (E) isn't phrased in a way that explicitly describes/establishes/dictates nested conditionals, it just gives you three sufficient conditions and one necessary condition. Trying to figure out valid ways to diagram it with nested conditionals isn't necessary to solve the problem and just makes things more confusing.

You should try to keep things as simple as possible instead of over complicating them in confusing ways. Using compound conditions with AND/OR connectors is much easier to put together properly without messing things up and is much easier to understand and apply properly on the fly without having to do more analysis than is necessary by having to deal with figuring out and analyzing nested conditionals.

Nested conditionals can be unnecessarily confusing since they add extra layers of difficulty/opportunities for mistakes working the question that you can avoid by keeping things as simple as possible. Figuring out and properly applying the contrapositive of nested conditional chains requires more analysis/can be very confusing/is much more susceptible to making mistakes since properly converting ANDs to ORs and vice versa with nested conditionals is much less straightforward than doing it with a straight up single compound conditional where you can just reverse and negate everything fairly brainlessly/without having to think really deeply about it.

Another recent LR question with tricky conditional logic is PT61 S4 #26

It's a parallel flaw question with numerous tricky uses and constructions of conditional premises not only in the stimulus, but in the answer choices too. There are a few instances of nested conditionals in that question as well as some other fun funky conditional reasoning twists worth reviewing thoroughly to see the various tricky things they did in each of the answer choices to make it extra hard. The flawed pattern of reasoning in the stimulus is super rare in LSAT history, I don't think it's ever been done in a parallel flaw Q before and only vaguely remember having seen it once before in an old question but am not positive. It's not just a basic run of the mill conditional reasoning flaw. Let me know if you figure out what the flawed pattern specifically is logically, most people that get it correct do so via POE and never really understand specifically what the flaw is/cannot describe it specifically in logical flaws terms.

[mymrh1]

Hi Jeffort, Christine,

Original statement: "a bill that most people favor will be passed promptly into law in a well-functioning democracy if the bill does not violate anyone's basic human rights."

I can see one should diagram the above statement as:

If Bill doesn't violate basic rights AND Most people Favor Bill AND a well functioning democracy ---> then Bill will pass promptly

However, it started to confuse me (as you said it would), when you started writing it as nested conditional within another conditional using three sufficient conditions (Bill doesn't violate basic rights, Most people Favor Bill, a well functioning democracy).

Is it true that one can write conditional statements using those three sufficient conditions (Bill doesn't violate basic rights, Most people Favor Bill, a well functioning democracy), but those different conditional statements are logically equivalent?

For example,

1. Well functioning democracy --> (Bill doesn't violate basic rights AND Most people Favor Bill ---> Bill will pass promptly)

2. If well functioning democracy --> (if bill doesn't violate basic rights ----> (Most people favor bill ---->bill will pass promptly))

3. If bill doesn't violate basic rights ---> (well functioning democracy AND Most people Favor Bill ---> Bill will pass promptly)

Are all 3 above logically equivalent?

#3 is how I would diagram before seeing this post.

Thank you!