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#19 - In West Calverton, most pet stores sell exotic birds

Clay Cooper
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Hi al_godnessmary,

Thanks for your question.

Yes, you mistook a sufficient condition for a necessary condition. We are told that any store that sells tropical fish but not exotic birds sells gerbils. So:

fish + ~birds :arrow: gerbils.

But it sounds like you misread that as ONLY those stores which sell fish but not birds sell gerbils, which would look like this:

gerbils :arrow: fish + ~birds

and would give us the contrapositive,

birds or ~fish :arrow: ~gerbils.

I think that is the source of your mistake.

Remember, to say 'any X is Y' and to say 'only X are Y' are two very different statements. I think what you did here was confuse the two.

I hope that helps.
janietoto1029
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Hi,

I diagrammed this as the following -

(1) PS :most: EB :most: TF
(2) TF + ~EB :arrow: G
(3) G :arrow: ~PSI (independent PS)

Answer choice D essentially seemed to capture the inference following from combining (2) and (3) TF + ~EB :arrow: ~PSI

Is this the right way to go about this q?

Thanks!
James Finch
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Hi Janie,

Yep, looks perfect! A lot of the more difficult Must Be True questions will throw in irrelevant premises (like the formal logic chain we have here), but keep the scope in mind and realize what has to be true. Given that this is a 100% certain MBT question, the conditional chain is what we should be looking for, exactly what you did. Good job!
T.B.Justin
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Pet stores ..... :most: ..... Exotic birds ..... :most: ..... TFish

The author then presents a somewhat complicated conditional rule: that if a pet store sells tropical fish, but not exotic birds, then it must sell gerbils. Further, any store that sells gerbils is not an independently owned West Calverton pet store:

Tropical fish
..... + ..... ..... :arrow: ..... Gerbils ..... :arrow: ..... Independently owned WC pet store
Exotic birds


Can this be diagrammed as follows:

Pet stores :most: Exotic birds :most: TFish :arrow: Not exotic birds :arrow: Gerbils :arrow: Not Independent
AM4747
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Hello,

Just a question about diagramming "but" statements. I am aware that diagramming in this particular question might not be the best course of action; but learning it may be useful in other contexts.

In particular, correct answer choice D states: "No independently owned pet store sells tropical fish BUT not exotic birds".

This statement has one sufficient condition and two necessary ones. Intuitively, in diagramming, I negate:

Independent Stores ----> NOT tropical fish OR Exotic birds.

This is how I work thing out intuitively. But more explanation would be deeply appreciated.

All best
T.B.Justin
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AM4747 wrote:Hello,

Just a question about diagramming "but" statements. I am aware that diagramming in this particular question might not be the best course of action; but learning it may be useful in other contexts.

In particular, correct answer choice D states: "No independently owned pet store sells tropical fish BUT not exotic birds".

This statement has one sufficient condition and two necessary ones. Intuitively, in diagramming, I negate:

Independent Stores ----> NOT tropical fish OR Exotic birds.

This is how I work thing out intuitively. But more explanation would be deeply appreciated.

All best


Hey AM4747,

I believe that it is

Not tropical fish or Exotic birds :arrow: Independent store

Edit:

I think your conditional representation is the CP of the last conditional statement in the stimulus and that is correct. Mine is a mistaken negation :)

I thought you changed "but" to "or" instead of "and," so that's how I made that mistaken negation!

Thanks for the learning experience!
Adam Tyson
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AM4747 - exactly right! T.B. Justin - good that you caught yourself there and bravo for learning from the experience!

Answer D is saying that if a pet store in West Calverton is independent, then it either does NOT sell tropical fish, or else it DOES sell exotic birds. That would also allow for both things to be true - it could sell no tropical fish and still sell the birds. What would be impossible is for such a store to sell tropical fish and not sell exotic birds, because then it would have to sell gerbils, which independent stores do not sell. The "no" at the beginning of that answer choice negates the necessary conditions, leaving the sufficient condition in the positive form - if X, then NOT Y and Z (so either Y or Z must occur, perhaps both).
Adam M. Tyson
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T.B.Justin
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Thanks Adam!