by ohthatpatrick Wed Mar 08, 2017 8:07 pm
Sure thing.
The original argument is basically:
p1: A --> B
p2: B --> C
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c: ~C --> ~A
To get this most easily, you have to know how to translate "No A's are B's".
If we say "No NFL players are female", how would that look as an "if/then"?
If you're NOT an NFL player, then you're female
or
If you're an NFL player, then you're NOT female
No A's are B's = All A's are not-B's
(in a similar manner, Not All A's are B's = Some A's are not-B's)
So in this argument,
p1: gourmet cook --> enjoy wide variety
p2: enjoy wide variety --> do not prefer bland
At this point, we should see the chain:
gourmet cook --> enjoy wide variety --> do not prefer bland
and its contrapositive
DO prefer bland --> do not enjoy wide variety --> not gourmet cook
conc: DO prefer bland --> not gourmet cook
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Again, it's a valid argument:
It provides two conditional premises that form a A -> B -> C chain,
and then it concludes ~C --> ~A
If any of these answers do not have two conditional premises that chain together, we'll stop reading.
If we DO get an A -> B -> C chain, we'll know to expect ~C -> ~A in theh conclusion.
------------------
(A) Not a valid inference.
The first two ideas don't create a perfect chain, because the first idea is saying "if you're a painting in the HC, you'll be put up for auction next week."
The second idea is saying "if you are the collection of paintings to be auctioned next week, you're by a wide variety of artists".
We can't infer that each painting in the HC is by a wide variety of artists, nor can we infer that the set of painting in the HC is by a wide variety of artists.
It's possible that all the paintings in the HC are by the same artist. That wouldn't contradict anything we're told.
(B) YES! Two premises chain together and the conclusion is ~C -> ~A
chain: in HC -> abstract -> not included in next week's auction.
conc: included in next week's auction --> not in HC
(C) These premises don't chain together.
p1: in HC --> superb
p2: in HC --> not by Roue
Move on.
(D) These premises don't chain together.
p1: Postimpression and in HC --> auctioned next week
p2: Pop art and in HC --> not auctioned next week
Move on.
(E) These premises chain, but the conc doesn't match.
p1: in HC and auctioned next week --> major work
p2: major work --> no price can adequately reflect value
We need a "~C -> ~A" conclusion, or
"If the price DOES adequately reflect value, then you're not an HC painting slated to be auctioned next week"
Hope this helps.