Biconditionals

James Dean

Perhaps I missed something as I do not remember a lesson on biconditionals (double arrows).

My understanding is that each term is both sufficient and necessary for the other.

Here are some indicators that I've noted:

A or B, but not both

A if, but only if B

A if and only if B

A when, only when B

If A, then B, vice versa

If A, then B, otherwise not

Except A, B




I have seen J.Y. mention "except" and "otherwise" in a video, but I am confused in regards to their usage as a biconditional indicator. In the past I've categorized "except" as a group 3 indicator, so that is causing issues in my thought processes.

Would someone elucidate these?

Also, list any other biconditions indicators/ tips that you've encountered.

Thanks,

JD

CJ Shin

I am not quite sure what you are asking about bi-conditionals, but the important takeaway from those lessons is that bi-conditionals are 2 types:

1. Always together, never apart (A<->B).
2. Always apart, never together (A<->/B).

The knowledge of this is crucial in in-out games with lots of conditions chaining up because it really makes your life easier lol.

For example, the premises are:

1. If A, then B (A->B)
2. B only if C (B->C)
3. If C, then D, but not otherwise (C<->D)

Chaining these up you get: A->B->C<->D.

Suppose a question asks you; if C is out, how many elements can be in?
The answer to this questions is 0.

Can you figure out why?

As for except.. my experiences tells me that it is really vague in the sense that it is more intuitive than mechanical..

James Dean

I know my question, if there is one, is vague. That's the thing, I don't remember biconditionals being explained in the lessons. Granted, I've only completed 60% of the lessons, so they may be covered in one of the games sections. So, what I listed is what I've gathered through my own observations.

Your response is very helpful, and I believe it was the missing link that I needed to make things "click".

Thank you for your reply.

CJ Shin

James, my pleasure.
Don't worry too much about bi-conditionals for LR.
They are very rare and even if they do pop up as one of the MBT questions, they are pretty easy to spot.

But for games, you must be able to chain them up with other conditions, and know precisely how they interact when one of the elements are kicked in or out.

It takes time to get used to them, just practice practice.

lsat 1101

Hello,
Your videos have been so helpful. I also find the question above so helpful because it lists some weird rules I had not encountered before. I still would appreciate if someone could let me know if I've translated them correctly below. I just don't understand the "but not otherwise" and how that translates to a <-> relationship either.

A or B, but not both: A<->/B

A if, but only if B: A <-> B

A if and only if B: A <-> B

A when, only when B: A <-> B

If A, then B, vice versa: Does that also mean A <-> B?

If A, then B, otherwise not: ? why or how does that mean <->

Except A, B: ?? I have no idea what to make of this? A game context would help with understanding this

The 180 Bro_OVO

I'm not sure about "if A, then B vice versa" and "except A, B"

@Sami

What are your thoughts?

Sami

@"The 180 Bro_OVO" said:

I'm not sure about "if A, then B vice versa" and "except A, B"

@Sami

What are your thoughts?

Hey : )

So yeah, if A, then B vice versa would imply a bi-conditional relationship. "Vice-versa" just means to reverse whatever was said, so in this case it would be if B, then A. Which combined with the first statement would mean: A<----->B.

I honestly don't think except A,B implies a bi-conditional relationship. I have yet to encounter it and even grammatically it does not add up to mean the same thing. But just for a second set of eyes lets get @"Cant Get Right".

Cant Get Right

I'm not sure what "except A, B" means. I'll assume we mean "B except when A." It's an interesting statement. So let's think about what it means.

It seems to imply that we must have B in the absence of A:
Except when A, B.
/A --> B

But it carries the simultaneous implication that when we do have A, we do not have B.
When A, not B
A --> /B

So no matter what value we assign to a given variable, one of these conditionals is triggered. A or /A will satisfy one of our two sufficient assumptions. B or /B will trigger one of our contrapositives. So this does seem to function as a bi-conditional.

A <--> /B

Really interesting construction. I don't immediately recognize the structure, but by breaking down the language, that seems to be the logical implication. Does anyone see any issues with this analysis? I'm not 100% sure, so I'd welcome any input or challenges to my reasoning.

Sami

@"Cant Get Right" said:
I'm not sure what "except A, B" means. I'll assume we mean "B except when A." It's an interesting statement. So let's think about what it means.

It seems to imply that we must have B in the absence of A:
Except when A, B.
/A --> B

But it carries the simultaneous implication that when we do have A, we do not have B.
When A, not B
A --> /B

So no matter what value we assign to a given variable, one of these conditionals is triggered. A or /A will satisfy one of our two sufficient assumptions. B or /B will trigger one of our contrapositives. So this does seem to function as a bi-conditional.

A <--> /B

Really interesting construction. I don't immediately recognize the structure, but by breaking down the language, that seems to be the logical implication. Does anyone see any issues with this analysis? I'm not 100% sure, so I'd welcome any input or challenges to my reasoning.

Oh that makes so much more sense when we write down it in "B except when A". I was so confused what "except A,B" even meant to begin with. Thanks!

lsat 1101

Thank you so much everyone!!