Diagraming Or and Not-Both

[chike_eze]

I hope I have not posted this before, or have not responded to someone who posted this before. If the former or latter, but not both, is the case, then I only apologize for the former if it is indeed the case.

This brings me to my question. It has to do with how to diagram "either/or + not both" conditions.

I get that "X or Y" is diagrammed as not Y -> X and
"not both X and Y" is diagrammed as X -> not Y

Therefore, X or Y but not both is diagrammed as X <-> not Y

But what about, If X then Y or Z but not both?
Does this translate to: X -> Y <-> not Z

Not sure that makes sense to me, or even if it does, how do I get the contrapositive of that statement? Maybe I'm missing something.

It makes more sense (still makes my head hurt) to write it out like this:

X -> YorZ and not(YandZ)
X -> YorZ and (notY or notZ)
Or
X -> YorZ
X-> notY or NotZ

Contra:
notY and notZ -> notX
Y and Z -> notX

Thoughts??

Note: This was a crucial condition in SuperPrep-B Game 2. Check it out.

[patrice.antoine]

It's been ages since I revisited LSATs and have picked up the mantle again but my understanding is:

If X --> Y & ~Z OR If X --> Z & ~Y

And the contrapositive of those are (remember, the contrapositive of "AND" is "OR":

If Z OR ~Y --> ~X OR If Y OR ~Z --> ~X

I could be wrong though. It's quite possible to have XY, XZ, and YZ together, just not XYZ all together.

[timmydoeslsat]

It makes more sense (still makes my head hurt) to write it out like this:

X -> YorZ and not(YandZ)
X -> YorZ and (notY or notZ)
Or
X -> YorZ
X-> notY or NotZ

Contra:
notY and notZ -> notX
Y and Z -> notX

Thoughts??

Note: This was a crucial condition in SuperPrep-B Game 2. Check it out.

It was absolutely a crucial condition in that game.

This is the way I diagram it.

X ---> 1 X/Y in, 1 X/Y out.

The contrapositive is that if you have a situation of both in or both out, you know X is out.

[chike_eze]

@Tim, that makes sense.

I find myself usually wasting time convincing myself which case it is -- both can't be in or both cant be out.

X or Y
- at least one in or both in

not both X and Y
- at least one out or both out