Strange wording of an "or/and" conditional (fruit stand gam)

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Easy-E
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Joined: Fri Feb 18, 2011 1:46 pm

Strange wording of an "or/and" conditional (fruit stand gam)

Postby Easy-E » Thu Jan 05, 2012 9:45 am

I'm fairly sure that this is just an unnecessary way of wording a relatively simple conditional, but its kind of tripping me up. I feel like most conditionals like this are worded to be exclusive (If A then either B or C but not both), but this seems to be inclusive (could be either one or both). Am I correct to assume that having W tells me I'll have either F, T, or both, but NOT having either of F or T means I can't have W. Just bit confused by this wording that I really haven't seen outside the fruit stand game.


"If the stand carries watermelons, then it carries figs or tangerines or both."

W-->F or T or FT

~F-->~W
~T-->~W




I guess the big clarification I need is whether a conditional with "or" is inclusive or exclusive, assuming its not noted somehow ("but not both").

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KevinP
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Joined: Sat Sep 26, 2009 8:56 pm

Re: Strange wording of an "or/and" conditional (fruit stand gam)

Postby KevinP » Thu Jan 05, 2012 10:25 am

emarxnj wrote:I'm fairly sure that this is just an unnecessary way of wording a relatively simple conditional, but its kind of tripping me up. I feel like most conditionals like this are worded to be exclusive (If A then either B or C but not both), but this seems to be inclusive (could be either one or both). Am I correct to assume that having W tells me I'll have either F, T, or both, but NOT having either of F or T means I can't have W. Just bit confused by this wording that I really haven't seen outside the fruit stand game.


"If the stand carries watermelons, then it carries figs or tangerines or both."

W-->F or T or FT

~F-->~W
~T-->~W




I guess the big clarification I need is whether a conditional with "or" is inclusive or exclusive, assuming its not noted somehow ("but not both").


If not indicated otherwise, or is always inclusive. In this case, the "or both" is completely extraneous; the statement could have very well just said "If the stand carries watermelons, then it carries figs or tangerines." You are incorrect to assume that if you don't have either F or T, then you don't have W. However, if you have neither F nor T, then you don't have W.

Here's a diagram:
W -> F OR T
~(F OR T) -> ~W (contrapositive)
~F AND ~T -> ~W (De Morgan's law)

Hope this helps.

User avatar
Easy-E
Posts: 5688
Joined: Fri Feb 18, 2011 1:46 pm

Re: Strange wording of an "or/and" conditional (fruit stand gam)

Postby Easy-E » Thu Jan 05, 2012 10:45 am

KevinP wrote:
emarxnj wrote:I'm fairly sure that this is just an unnecessary way of wording a relatively simple conditional, but its kind of tripping me up. I feel like most conditionals like this are worded to be exclusive (If A then either B or C but not both), but this seems to be inclusive (could be either one or both). Am I correct to assume that having W tells me I'll have either F, T, or both, but NOT having either of F or T means I can't have W. Just bit confused by this wording that I really haven't seen outside the fruit stand game.


"If the stand carries watermelons, then it carries figs or tangerines or both."

W-->F or T or FT

~F-->~W
~T-->~W




I guess the big clarification I need is whether a conditional with "or" is inclusive or exclusive, assuming its not noted somehow ("but not both").


If not indicated otherwise, or is always inclusive. In this case, the "or both" is completely extraneous; the statement could have very well just said "If the stand carries watermelons, then it carries figs or tangerines." You are incorrect to assume that if you don't have either F or T, then you don't have W. However, if you have neither F nor T, then you don't have W.

Here's a diagram:
W -> F OR T
~(F OR T) -> ~W (contrapositive)
~F AND ~T -> ~W (De Morgan's law)

Hope this helps.



:? Not sure how I mixed that one up to be honest, but thank you for the clarification! Got it now.




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