Diagramming/Understanding Conditional Reasoning Exception

svscire216
Posts: 2
Joined: Mon Dec 19, 2011 7:29 pm

Diagramming/Understanding Conditional Reasoning Exception

Postby svscire216 » Fri Jun 15, 2012 3:03 pm

Hello out there, TLSers -

I have Fridayitis at the office so I thought I'd pick your brains on a fun conditional I can't seem to wrap my head around right now (which also might have something to do with the whole Friday thing).

Arguments/Rules (not from any particular PT): If "x", then "y", except when there is "z", in which case there is never "y".

My diagrams:
X -> Y
Z -> Y
Y -> Z

Therefore...
X -> Y -> Z (or X -> Z)
Z -> Y -> X (or Z -> X)

Clarification: The given rules preclude the existence of X and Z together to yield Y, correct? In other words, "X or Z, never both"? The exception wording is a bit untidy.

Much appreciated. Enjoy the weekend.

VasaVasori
Posts: 573
Joined: Sun Dec 11, 2011 2:36 pm

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Postby VasaVasori » Fri Jun 15, 2012 3:08 pm

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Last edited by VasaVasori on Sat May 02, 2015 10:57 pm, edited 1 time in total.

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Noblesse_Oblige
Posts: 44
Joined: Mon Feb 06, 2012 7:41 pm

Re: Diagramming/Understanding Conditional Reasoning Exception

Postby Noblesse_Oblige » Fri Jun 15, 2012 3:20 pm

svscire216 wrote:Hello out there, TLSers -

I have Fridayitis at the office so I thought I'd pick your brains on a fun conditional I can't seem to wrap my head around right now (which also might have something to do with the whole Friday thing).

Arguments/Rules (not from any particular PT): If "x", then "y", except when there is "z", in which case there is never "y".

Enjoy the weekend.



Sorry, other people's diagrams confuse me, but this is how I would diagram that.
Z -> ~Y
Y -> ~Z

(X -> Y ) V ([X ^ Z] -> ~Y)
~Y -> ~X V (Y-> ~[X ^ Z]) (notice the limited effect of Y, It doesn't guarantee No X AND no Z, only no X AND Z at once)

I would circle the Z->~Y rule set to let me know it is more important, but I would also write out the V condition so I don't forget that the Z overrides.

ALSO:

"~" <------This is the mathematical conditional symbol for "Not" or "Negative" It is much less messy than crossing things off and will be helpful to know if you take logic math (Which is all about conditionals and probabilities)

Anyway, as long as YOU know the order of the rules, then everything is swell

I love games. I miss them already, may do one for fun lol

unitball
Posts: 64
Joined: Mon May 23, 2011 12:37 am

Re: Diagramming/Understanding Conditional Reasoning Exception

Postby unitball » Fri Jun 15, 2012 5:59 pm

X -> Y

Z<--I-->XY

that's how i'd throw it down

VasaVasori
Posts: 573
Joined: Sun Dec 11, 2011 2:36 pm

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Postby VasaVasori » Fri Jun 15, 2012 6:53 pm

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Last edited by VasaVasori on Sat May 02, 2015 10:57 pm, edited 1 time in total.

unitball
Posts: 64
Joined: Mon May 23, 2011 12:37 am

Re: Diagramming/Understanding Conditional Reasoning Exception

Postby unitball » Sat Jun 16, 2012 3:47 am

VasaVasori wrote:
unitball wrote:X -> Y

Z<--I-->XY

that's how i'd throw it down

I'd be careful with this, because YZ is still an acceptable combination per this diagram. That is, unless you interpret the latter part to mean Z can't be with X and Z can't be with Y - but in that case, the diagram is also incorrect.


you're right. i didnt read the rule correctly
Last edited by unitball on Sat Jun 16, 2012 6:03 pm, edited 1 time in total.

svscire216
Posts: 2
Joined: Mon Dec 19, 2011 7:29 pm

Re: Diagramming/Understanding Conditional Reasoning Exception

Postby svscire216 » Sat Jun 16, 2012 12:48 pm

It seems from your responses there are multiple ways to approach the phrasing of the question, and from there, to follow-up with a different (and by saying different, really just meaning preferential) way of diagramming and notating the statement. The next question then: For purposes of taking the LSAT, if I get an argument/rule that follows the convention above, should the given exception be considered to be in tandem with the sufficient condition (e.g., "X AND Z" or "X OR Z") to the argument when plotting out the deductions which may follow? My gut tells me 'yes', but I can't help to feel somewhere down the line that assumption coming back to haunt me as faulty reasoning.

Thanks for the help, guys!

unitball
Posts: 64
Joined: Mon May 23, 2011 12:37 am

Re: Diagramming/Understanding Conditional Reasoning Exception

Postby unitball » Sat Jun 16, 2012 6:06 pm

^ if that rule was given on the lsat, i would assume both principles work together.

so if Z was not included, and X is in, then both X and Y are in. if Z is in, X could also be in, but Y would have to be out.

SanDiegoJake
Posts: 149
Joined: Mon Mar 07, 2011 3:17 pm

Re: Diagramming/Understanding Conditional Reasoning Exception

Postby SanDiegoJake » Mon Jun 18, 2012 9:36 pm

x, ~z --> y
~y --> ~x / z

z --> ~y
y --> ~z

Legend: "," = "AND"
"/" = "OR"
"~" = "NOT"




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