by noah Tue Feb 02, 2010 12:39 pm
You're right to look for shifts in the way things are phrased (i.e. "many" vs. "all"), but (C) is primarily wrong for a different reason. Let's start by identifying the flaw in the original argument:
In brief, the argument is that only experienced salespeople will make their quota, thus I'm not experienced since I didn't make the quota.
The problem with this is that you may be experienced but NOT make the quota. What you do know is that if someone does make the quote, they are experienced.
[This would be like saying: Only those over 15 years old can be on the gymnastics team. Since I'm not on the gymnastics team, I must not be over 15 years old. Maybe I'm 14 but just not into wearing tights. ]
Diagrammatically, the argument says this:
make quota --> experienced
not make quota --> not experienced
boiling it down further:
q --> e
~ q --> ~ e
As you can see, this is a simple negation (which of course is a no-go in logic), not the contrapositive.
(B) has the same structure:
take class --> music lover
~ take class --> ~ music lover
The other answers are wrong for various reasons that all boil down to not matching the argument's flaw.
(A) casually dressed --> Friday
~ casually dressed --> Not going to work
This introduces some new elements to the argument. It should conclude that it's not Friday.
(C) enjoy the Atlantic --> oceanographer
~ oceanographer --> ~ enjoy the Atlantic
A-ha! This is a valid argument. It uses the contrapositive.
(D) giant redwood --> northern
redwood --> northern
Again, a valid argument. This one utilizes a simple application of the premise.
(E) El Capitan --> accomplished climber
accomplished --> El Capitan
This is an illegal reversal, not a negation. Being accomplished is a requirement for being able to climb El Capitan, but it's not sufficient for being able to do so. To "make" this one parallel, it should say "since she cannot climb El Capitan, Michelle must not be accomplished."