An air traveler in Beijing cannot fly to Lhasa without first flying to Chengdu. Unfortunately, an air traveler in Be...

Shememories December 16, 2013

Help!

Please explain. The logic I extracted was: L - >1stC Not1stC - >notL X - >not1stC 1stC - >notX C: L - >X I concluded the argument was invalid. Is that right?

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Mehran December 19, 2013

This argument is valid. Let's diagram together.

First premise: "An air traveler in Beijing cannot fly to Lhasa without first flying to Chengdu."

Remember "without" is treated just like "unless" so it introduces the necessary condition and the negation of the other part of the sentence is our sufficient condition. So our necessary condition here would be "flying to Chengdu" (aka "B2C") and our sufficient condition would be "an air traveler in Beijing CAN fly to Lhasa" (aka "B2L").

P: B2L ==> B2C
not B2C ==> not B2L

Second premise: "an air traveler in Beijing must fly to Xian before flying to Chengdu."

"Must" introduces a necessary condition so our necessary condition here is "fly to Xian" (aka "B2X") and our sufficient condition is "before flying to Chengdu" (aka "B2C"). This means if a traveler flies from Beijing to Chengdu, then they traveled from Beijing to Xian.

P: B2C ==> B2X
not B2X ==> not B2C

Conclusion: "Any air traveler who flies from Beijing to Lhasa, therefore, cannot avoid flying to Xian."

"Any" introduces a sufficient condition so our sufficient condition here is "air traveler who flies from Beijing to Lhasa" (aka "B2L") and our necessary condition is "cannot avoid flying to Xian" (aka "B2X").

C: B2L ==> B2X
not B2X ==> not B2L

We can use the transitive property to connect the first and second premise: B2L ==> B2C ==> B2X. From this we can conclude: B2L ==> B2X (or the contrapositive not B2X ==> not B2L). So, this is a valid positive transitive argument.

Hope this helps! Please let us know if you have any other questions.

TheFacu March 26, 2015

Dont u have to negate b2x in the conclusion? Since it says: "cannot"

Naz March 27, 2015

I see your confusion here, but the conclusion says: "cannot avoid," which is essentially a double negative. The conclusion is saying: any air traveler who flies from Beijing to Lhasa, must have flown to Xian, as well.

Hope that clears things up! Please let us know if you have any other questions.

Tony October 5, 2018

Can some one explain to me why A isnt the answer as it seems to follow the same transitive property as the PR. Could it be because of the "either" and "or"