no X builds Y but not Z

alexroark5

How would you guys diagram this statement?

jdawg113

if Y & /Z -> /x (i think)lol took me a minute to make sense of that, its saying X cannot build Y without building Z too

Alex Short

Hey Alex - how's it going? Long time no see - we should meet up sometime. I would look at this statement as "X builds Y, but not Z", with the 'No' negating all elements that follow.

I understand "X builds Y, but not Z" much more easily, and would write it as a single X with two arrows, one to Y and another to ~Z.

If there is no comma in the statement, I'd have to assume the "No" at the beginning applies to both elements.

So, "No X builds Y":
X -> ~Y

And "No (X builds Not Z)"
(X -> ~Z)
~X -> Z

Ultimately getting:

X -> ~Y and ~X -> Z

Although, admittedly, I'm certainly uncertain about my approach in this case.

Alex Short

jdawg's approach was the other route I imagined possible... but I hesitated with that approach only because the grammar trips me up with this particular phrasing (aka, the lack of a comma). Good to know!

jdawg113

@"Alex Short" idk, that makes it look like X can't build Y and Z which isn't how I see it. I see it as X can build Y and Z but cannot build Y if it doesnt also build Z

Alex Short

@jdawg113 Okay, that makes much more sense for me - I saw both as possibilities but I thought that

"X can build Y and Z but cannot build Y if it doesnt also build Z"

would be written as "No X builds Y, but not Z". And with that, time for some coffee! Thanks for the clarification though; I appreciate it!

Catehm88

It is saying that if X builds Y, then it must also build Z take out the negative language on this one.

(X-->Y)--> (X-->Y&Z)

The contrapositive of the statement is, if X does not build Z then it does not build Y.

I hope this helps a little.

jdawg113

eh its similar... and I like the wording you used there @Catehm88

blah170blah

Wait, I'm actually confused lol. I understood this statement to mean two things:
1) no X builds Y (Y --> /X)
2) no X does not build Z ( Z --> X)

Y --> /X
/X --> /Z
-----------
Y --> /Z

Is that not right? lol

jdawg113

@blah170blah I don't think so. think of it as no X builds Y without(but not) building Z

blah170blah

Ahhh I see. So we have two conditions for the conditional.

If you have Y AND /Z then you don't have /x.

Which is what you said:
Y & /Z ---> /X

Matt1234567

I take it as If it is X and it builds Y, it must build Z.

jdawg113

@Matt1234567 yes