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I'm not understanding the difference between these two rules
lsat 1101
Alum Member
X <-> ~Y
X -> ~Y
Could someone please clear up for me? Thanks!
Comments
x <->~y is if x then not y and if not y then x
x->~y is if x then not y
Thank you very much for your help, I'm still not understanding it visually though. could we have a diagram that represented both rules to show that for example, x is out, and y is free to float, either in the in or out group? Because the second rule i wrote can be contraposed (to y then not x) wouldn't that make it the same as the first rule I wrote?
@needmylsat180 is correct.
Another way to think of it.... For the first one:
X <-> ~Y
If you have "x", then you MUST have "~y"
And if you have "~y", then you MUST have x.
This is often referred to as a bi-conditional.
You should consider viewing this lesson. Very informative.
https://7sage.com/lesson/advanced-bi-conditionals/
Now for the second one. X -> ~Y
That is not a bi-conditional.
If you have "x", then you MUST have "~y".
However,
If you have "~y", it is NOT necessary for you to have "x".
This is just a straight forward logical relationship.
Consider this video for that.
https://7sage.com/lesson/logical-indicators-and-translations/
Does this help?
Since the arrow goes both ways to see it in its simplest manner we can break it down two conditional statements as the arrow goes both ways:
So X <-->~Y can be broken into:
X--->~Y and ~Y--->X (since the arrow goes both ways)
Now lets do a contrapositive for these two statements above:
Y--->~X ; ~X---->Y
Now lets take a look at this one. Unlike the conditional chain on top which could be split into two because we only have an arrow that goes one direction this chain cannot be split and we can only conclude the statement itself and its contrapositive:
X-->~Y
Y--->~X (its contrapositive)
*That's it. We only have two possible chains here unlike the four conditional chains which we could conclude from the bi-conditional chain on top.
Let me know if this helped.
Thank you both. I've been studying logic games for a while now but just discovered 7sage and am still deciding if I want to purchase the course so at the moment I don't have access to those lessons. I've been watching JY's videos which have helped so much but my confusion happened today when I was watching one of his videos and the X <-> ~Y rule came up. Up until now he's been stressing to look for all the not both relationships X -> ~Y. I'm a little embarrassed, I thought I knew my straightforward logical relationships, I do understand that you can't reverse and say not y gives x. I'm just trying to understand JY's inferences he's applying to in out games and setting up the initial board. he puts "x/y" in the out slot. and then says the other is free to float in the in group OR it can be out as well. I'm just trying to understand visually, if this applies to just one or both rules?
Hey so no need to be embarrassed.
We all had to learn this at one time or another. It takes courage to ask and open up to others about what you don't know. Thank you so much for asking 
. I am so glad you did 
.
Now Lets try to understand this question from the in-out perspective for each of the two rules. Lets do the X--->~Y first.
If X--->~Y
we know its contrapositive: Y--->~X
So when X is in when know Y is out.
contrapositive: Y is in then X is out.
That's it. We can't conclude anything about when Y is out or X is out.
Because when Y is out, our chain above (arrow) doesn't trigger so X is free to float in or out.
Similarly when X is out our chain doesn't trigger and Y is free to float and can be in or out.
Now lets take a look at our bi-conditional statement.
X<----->/Y
for learning purposes lets break down our two arrows more simply:
X--->~Y and when ~Y----->X
The contrapositive of X--->~Y is Y--->~X
The contrapositive of ~Y--->X is ~X----->Y
So when X is in Y is out
and when Y is in we have an arrow that says X is out
When X is out we have an arrow that says Y is in
and when Y is out we know X is in.
In other words all four of our possibilities are known for X and Y (in and out) in a bi-conditional whereas for the first one we didn't know what would happen for two of them.
based on the four statements above you can break down this in-out game into two possibilities. Take either X or Y and use it as a base. For us lets do it with X.
X is in Y out
X is out Y in
That's it. There are no more scenarios and your game board was neatly split into two worlds because of this bi-conditional rule.
I hope this helped a bit more.
I was googling and found someone who has written on these below - is this a correct interpretation?
with the second rule, you can't have either x or y be floaters? I don't know why this is confusing me but to me it sounds equivalent to say that "either x and y or both are out" and "either x or y but not both is in"??
Rule: X -> ~Y
Inference: Either X or Y or both are out
Master Game Board:
In Group Out Group Floater
X/Y Y/X
Rule: X <-> ~Y
Inference: Either X or Y but not both is in
Master Game Board: A good place to split master game board
Game Board #1:
In Group Out Group Floater
X Y
ugh sorry the table format got screwed up and does not show up properly when I copied and pasted here
So with this rule basically at most only one of X or Y can be in the in group. But when all we know is that either one of X or Y is out the other one is free to float and can be in or out. So with this rule you have four possibilities.
If we know:
X in then we can conclude Y out
if Y in X out
if Y out (X can be in or out so is a floater)
if X out (Y can be in or out so is a floater)
Thank you so much Sami for your kindness compassion and help
I think I hit enter and wrote my comment right after you had written yours so I didn't see it. I really appreciate that you wrote it all out, it helps especially the last paragraph. I'm just so visual, I'm going to go back to that video and look for the exact moment I got confused and try it again.
ahh thank you Sami your second explanation helped too I finally get it, I appreciate it!!! now if only I could understand the other one visually with respect to floaters!
You are welcome
and thank you for asking. I also thought we might have both hit enter together.
And I am visual too and its definitely an asset in learning Logic games. I think its a great idea to go back to that video and find out what confused you and learn this.
Keep us updated on your progress and good luck!!!
Oh I see my confusion now. . You said when we DO know. my worry has been how to set it up when we don't know, i.e. right at the diagramming phase. only the questions establish if it's in or out, otherwise we have a bare diagram with x/y in the out slot. And i'm back where I started
lol. nevermind thank you again
Hey so the bi-conditional rule doesn't have floaters : )
X<--->~Y
Contrapositive: ~X<--->Y
If X is in Y out
if Y is out X is in (as the arrow goes the other way)
if X is out Y in
if Y is in X is out (double arrow)
You can even simplify this further and only make two game boards since there are no floaters in conditional.
one game board: X is in.
second game board: X is out.
Homework:
(only if you want to)
write down the four game boards. X is in and X is out. Y is in and Y is out. And if you can tell me how we only end up with two game boards instead of four.
Ahh thank you so much
Seriously, I appreciate your time and help, I'm so glad that confusion came up otherwise I would have gone on thinking I have a basic grasp of these. beautifully explained, I did the homework, and I see what you mean, two boards are identical so I see now why the game board can be split in two worlds. Could I just ask, for Sami or anyone else who can answer, then x<-> y means both in or both are out, right? So we can also have two game boards that represent all worlds.
and sometimes I see people write x<-> with a vertical dash over the middle of the arrow, is that just another way of writing X<--->~Y?
thank you so much for your time
Honestly, my pleasure. I loved the way you wanted to learn with so much enthusiasm and curiosity. : )
and yes X<--->Y means both are in or both are out! I think you got this!
how sad, I thought I understood all this, then I did a game today that 's supposed to be SO easy PT 48 game 1, and I immediately did the first few rules as biconditionals instead of straight forward conditional. there are only two groups and h and r must be in one or the other, and they can't be together, so..?
:(
Hey,
It's okay. That happens the good thing is you are learning. None of the rules of that game imply a bi-conditional relationship. I remember when I first started I would memorize how the bi-conditional language actually sounded like and would go through flash cards daily for them. I even had them for sufficient and necessary conditions. You will eventually learn this and it can take a bit of time because its a bit like learning a new language. So don't feel sad
Thank you
I must be really tired. I just realized they could both be out, neither of them have to be in at any point. is that it?