## Wouldn't this be better noted as a biconditional?

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Journey180

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Joined: Wed Apr 17, 2013 5:22 pm

### Wouldn't this be better noted as a biconditional?

Do you remember the LGB example that says "each rock classic is preceded by a new composition"? It explains that this is properly noted as " R-->[NR]". This makes almost perfect sense because, when we get an R, we automatically get N right before that said R. However, it is not perfect because isn't having "[NR]" or "N going right before R" also a sufficient condition for having "R"? this may seem trivial to most or may not matter but I am looking for those who may understand what I am trying to say and understand that it would be helpful to clear up this little nit=picky logical reasoning detail: Wouldn't this be better said as " R<--->[NR]"? Furthermore, wouldn't the contrapositive of "R--->[NR]" be " -[NR]---> -R" ? In short, by saying " R--> [NR]", we leave the logical possibility that -R can still produce [NR]. Does this make sense? lol

The LSAT Trainer

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### Re: Wouldn't this be better noted as a biconditional?

If I understand correctly how you are thinking about this, it's actually something that I've heard from other students as well, so let me see if I can help --

The short answer is no --

The reason is because the "biconditional" aspect you discuss isn't really any information at all.

It's kinda like saying "If I know the website has blue and yellow, then I know it has blue." The consequence isn't really anything new to figure out, and doesn't need to be mentioned. By your same reasoning, knowing we have an NR also tells us that we have an N. We don't need to notate that.

Again, not sure if I understand you correctly, so if this doesn't relate to what you meant, sorry , but I hth -- MK

Journey180

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### Re: Wouldn't this be better noted as a biconditional?

The LSAT Trainer wrote:If I understand correctly how you are thinking about this, it's actually something that I've heard from other students as well, so let me see if I can help --

The short answer is no --

The reason is because the "biconditional" aspect you discuss isn't really any information at all.

It's kinda like saying "If I know the website has blue and yellow, then I know it has blue." The consequence isn't really anything new to figure out, and doesn't need to be mentioned. By your same reasoning, knowing we have an NR also tells us that we have an N. We don't need to notate that.

Again, not sure if I understand you correctly, so if this doesn't relate to what you meant, sorry , but I hth -- MK

Thank you for your reply. I understand that " If the website has blue and yellow, that it has blue" or "B&Y---> B" I also understand that this relates to my original problem because knowing "[NR]" lets us know we have "R" or " NR---> R". But, in your website having blue and yellow example, I don't know if it works the other way, meaning if your example is a two-way street. Because, if we know that the website has blue, we don't necessarily know that it also has yellow or we don't know that " B--->B&Y"...So.. the bi-conditional would not apply in that example. However, in my original problem..."R" does necessitate " [NR]" and vice versa. So, " R---> [NR]" and "[NR]--->R". I hope I am making sense.

ScottRiqui

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### Re: Wouldn't this be better noted as a biconditional?

Journey180 wrote: So, " R---> [NR]" and "[NR]--->R". I hope I am making sense.

But saying that [NR]---->R literally adds no information. You may as well write down [NR]---->N while you're at it; it's equally true.

It's useful to say "If you have an apple, then it's a red apple" A----->RA. But it's useless to say "If you have a red apple, then you have an apple" RA----->A.

So while I think you may be correct that you're describing a biconditional statement, I don't think that it's worth expressing it that way.

Journey180

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### Re: Wouldn't this be better noted as a biconditional?

ScottRiqui wrote:
Journey180 wrote: So, " R---> [NR]" and "[NR]--->R". I hope I am making sense.

But saying that [NR]---->R literally adds no information. You may as well write down [NR]---->N while you're at it; it's equally useful.

It's useful to say "If you have an apple, then it's a red apple" A----->RA. But it's useless to say "If you have a red apple, then you have an apple" RA----->A.

Yes. I was afraid I was gonna run into this objection. It is a valid objection that the biconditional may be ridiculous or maybe redundant. However, I hope my point still stands regardless. The truth is the truth ridiculous or not...right? lol

ScottRiqui

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### Re: Wouldn't this be better noted as a biconditional?

Journey180 wrote:
ScottRiqui wrote:
Journey180 wrote: So, " R---> [NR]" and "[NR]--->R". I hope I am making sense.

But saying that [NR]---->R literally adds no information. You may as well write down [NR]---->N while you're at it; it's equally useful.

It's useful to say "If you have an apple, then it's a red apple" A----->RA. But it's useless to say "If you have a red apple, then you have an apple" RA----->A.

Yes. I was afraid I was gonna run into this objection. It is a valid objection that the biconditional may be ridiculous or maybe redundant. However, I hope my point still stands regardless. The truth is the truth ridiculous or not...right? lol

The goal isn't to write down everything that's true; the goal is to write down everything that's true and potentially useful. Would you jot down X----->X for every element in a game? Why not? It's true.

In the example you gave, the only characteristic that makes it a biconditional is behavior that adds no new information. So whether it's a simple conditional or a biconditional, you should diagram it as a simple conditional and treat it as such.

Journey180

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### Re: Wouldn't this be better noted as a biconditional?

ScottRiqui wrote:
Journey180 wrote:
ScottRiqui wrote:
Journey180 wrote: So, " R---> [NR]" and "[NR]--->R". I hope I am making sense.

But saying that [NR]---->R literally adds no information. You may as well write down [NR]---->N while you're at it; it's equally useful.

It's useful to say "If you have an apple, then it's a red apple" A----->RA. But it's useless to say "If you have a red apple, then you have an apple" RA----->A.

Yes. I was afraid I was gonna run into this objection. It is a valid objection that the biconditional may be ridiculous or maybe redundant. However, I hope my point still stands regardless. The truth is the truth ridiculous or not...right? lol

The goal isn't to write down everything that's true; the goal is to write down everything that's true and potentially useful. Would you jot down X----->X for every element in a game? Why not? It's true.

In the example you gave, the only characteristic that makes it a biconditional is behavior that adds no new information. So whether it's a simple conditional or a biconditional, you should diagram it as a simple conditional and treat it as such.

We agree. During the actual LSAT, we should notate as efficiently as possible. And, the consideration of unnecessary relationships will detract from that efficiency. Let it be known that I am not telling people to jot down all possible truths during the LSAT! That kind of strawmans my claim by the way lol

Anyway, aside from considerations about what should be done on the LSAT and going back to the logical merit of the original claim, the particular example is not perfectly noted as " R--->[NR]" but you say it is most efficiently noted as such. I claim that it is not inaccurate to note " R <---> [NR]" for the said rule. So, I admit only your objection that it may be inefficient. And, I recognize that you admit that the bi-conditional does have merit.

At the end, I think there may be some applications that I have not thought of yet. And, I do admit that it may seem nit picky and useless or even ridiculous to some. But, when I think of the application...I'll let you know! lol

magickware

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### Re: Wouldn't this be better noted as a biconditional?

Journey180 wrote:
Wouldn't this be better said as " R<--->[NR]"? Furthermore, wouldn't the contrapositive of "R--->[NR]" be " -[NR]---> -R" ? In short, by saying " R--> [NR]", we leave the logical possibility that -R can still produce [NR]. Does this make sense? lol

How?

-R doesn't mean to any conditionals at all. The conditional is specifically R->NR. Making any sort of conclusions from -R is a mistaken negation...

Journey180

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### Re: Wouldn't this be better noted as a biconditional?

magickware wrote:
Journey180 wrote:
Wouldn't this be better said as " R<--->[NR]"? Furthermore, wouldn't the contrapositive of "R--->[NR]" be " -[NR]---> -R" ? In short, by saying " R--> [NR]", we leave the logical possibility that -R can still produce [NR]. Does this make sense? lol

How?

-R doesn't mean to any conditionals at all. The conditional is specifically R->NR. Making any sort of conclusions from -R is a mistaken negation...

We make no such conclusion from -R

magickware

Posts: 359
Joined: Sun Nov 04, 2012 1:27 pm

### Re: Wouldn't this be better noted as a biconditional?

Journey180 wrote:We make no such conclusion from -R

You're not, but I'm having a hard time following what you meant here-

"In short, by saying " R--> [NR]", we leave the logical possibility that -R can still produce [NR]. Does this make sense? lol"