Help! Conditional Logic... "When" Forum

[lijun]

I'm having the hardest time understanding this.

"Erica will buy the car when Mike pays for the insurance."
The right diagram of this is
M --> E
-E --> M

But, I can't understand why it is not
E --> M
-M --> -E

Because if Erica bought the car we KNOW that Mike pays for the insurance right?? Thus, E --> M .
I mean, what is the scenario where Erica buys the car and Mike does not pay for the insurance since we're told she buys it when he does...

So confused, please help!

[kaiser]

Where did you find this statement? This from an actual exam?

[Clearly]

I'm having the hardest time understanding this.

"Erica will buy the car when Mike pays for the insurance."
The right diagram of this is
M --> E
-E --> M

But, I can't understand why it is not
E --> M
-M --> -E

Because if Erica bought the car we KNOW that Mike pays for the insurance right?? Thus, E --> M .
I mean, what is the scenario where Erica buys the car and Mike does not pay for the insurance since we're told she buys it when he does...

So confused, please help!

Because it's not accurate, Erica could very well buy a car with or without m paying for insurance, all we no is that if Mike does pay for insurance, Erica will buy a car.

[lijun]

Where did you find this statement? This from an actual exam?

From a prep course

[lijun]

I'm having the hardest time understanding this.

"Erica will buy the car when Mike pays for the insurance."
The right diagram of this is
M --> E
-E --> M

But, I can't understand why it is not
E --> M
-M --> -E

Because if Erica bought the car we KNOW that Mike pays for the insurance right?? Thus, E --> M .
I mean, what is the scenario where Erica buys the car and Mike does not pay for the insurance since we're told she buys it when he does...

So confused, please help!

Because it's not accurate, Erica could very well buy a car with or without m paying for insurance, all we no is that if Mike does pay for insurance, Erica will buy a car.

Oh, okay! Thank you! I think this helped me understand my misunderstanding. It still kinda comes and goes, but I think I get it!

[TheMostDangerousLG]

When = if. It introduces a sufficient condition. Just for future reference.

[ihill]

What helps me when thinking about conditional logic is to simplify the problem to a very simple example. For this, I'd say something like: "when Bob works, he makes money". you would obviously diagram it like this W-->M and ~M-->~W as you can't work without getting paid. Just use the same language that the problem uses and apply it to a very simple statement. Over time, you want to get fast enough and comfortable enough with conditional logic so that you won't have to do this but when learning it, I find this technique helps.

[jselson]

When = if. It introduces a sufficient condition. Just for future reference.

Exactly. The sentence would have to be "Erica will buy the car WHEN AND ONLY WHEN Mike pays for the insurance" for it to be both necessary AND sufficient, as lijun assumes it is in the OP.

[ScottRiqui]

Part of the problem is that in spoken/written English, we often infer a biconditional from a conditional statement. If I were to say "If the weather is nice tomorrow, I'll take you to the beach", you might infer that if the weather's crappy, we're not going to the beach. And it would make sense - who wants to go to the beach when the weather's bad?)

But my statement was a conditional, not a biconditional. There was nothing in it that precludes a trip to the beach even if the weather is bad.

As pointed out, Mike obtaining insurance is sufficient for Erika to buy the car, but it's not necessary.


Also, in your very first post, you forgot to negate M in the contrapositive. The two correct statements should be

M --> E
-E --> -M

[Sourrudedude]

.

[Clearly]

I agreed with OP in my first read-through of the stimulus. Everyone else has explained why the right diagram is right, I put some thought into why OP's thought was wrong.

First, I think a lot of the confusion for this question comes from the phrasing of the stimulus. "Erica will buy the car when Mike pays for the insurance." At first the use of the word "the" made me assume that there was only one car, which makes the statement seem a lot like a biconditional: If Erika bought the car, then insurance had already been paid and if insurance is paid, Erika will buy the car. However, if you assume that there are multiple cars, Erika could buy a few of them without Mike paying for insurance. However, if this would be faulty logic.

The more important thing to note is that Mike never HAS to pay for insurance. Erica could just go ahead and buy the car while Mike sits on his ass.

In my experience, LSAC doesn't use ambiguous language like this as much as prep books do.

There is no way to interpret this in any way but the correct way. There is nothing ambiguous here, when introduces a sufficient condition.

[Sourrudedude]

.

[Clearly]

I agreed with OP in my first read-through of the stimulus. Everyone else has explained why the right diagram is right, I put some thought into why OP's thought was wrong.

First, I think a lot of the confusion for this question comes from the phrasing of the stimulus. "Erica will buy the car when Mike pays for the insurance." At first the use of the word "the" made me assume that there was only one car, which makes the statement seem a lot like a biconditional: If Erika bought the car, then insurance had already been paid and if insurance is paid, Erika will buy the car. However, if you assume that there are multiple cars, Erika could buy a few of them without Mike paying for insurance. However, if this would be faulty logic.

The more important thing to note is that Mike never HAS to pay for insurance. Erica could just go ahead and buy the car while Mike sits on his ass.

In my experience, LSAC doesn't use ambiguous language like this as much as prep books do.

There is no way to interpret this in any way but the correct way. There is nothing ambiguous here, when introduces a sufficient condition.

Clearly OP misinterpreted the stimulus or he would not have posted. We all sometimes misinterpret logical statements though, otherwise we would never miss any LR questions. When these mistakes happen, the TLS hivemind usually suggests two things: figure out why the right answer is right and why the wrong answer is wrong. In this case, I was trying to address the second part, which is less important in my opinion but still worth considering.

Edit: I realized that I repeated part of what you said in your first post - didn't mean to be redundant, my bad.

Redundancy is fine, heck half of TLS is just repeated shit. Figuring out why someone got something wrong is all well and good, but justifying why someone got something wrong only works in justifiable situations. How many cars the wording implies is irrelevant, there is no ambiguity here, and there is no implication of a biconditional nature either. The reality is the student needs to learn sufficient triggers better, which is great, they came to the right forum. I learned a lot of this stuff here my self a long time ago. People mess up logic all the time, no doubt, and there is nothing wrong with that, but trying to rationalize the mistake with faulty stuff is just going to confuse them more. Conditional logic is foreign enough without introducing things that don't matter, like how many cars there are.

ETA: Also, I'm really not trying to be rude, so sorry if it comes off that way, I'm just trying to clear the confusion.