« on: May 10, 2009, 12:47:42 AM »
Superprep's explanation of the second game on the Feb 1999 LSAT doesn't make sense to me. Superprep says that if firs are not in the park, then Laurels and Oaks must be in the park. The condition is "if it is not the case that the park contains both laurels and oaks, then it contains firs and spruces." Wouldn't the contrapositive be if not spruces or firs then laurels or oaks?
Not quite, with the contrapositive. There are a coupla logically equivalent ways to read the first part of the condition. It's not saying "if not laurels and not oaks then..." It's saying "if not both" in other words: if there are not laurels OR not oaks, then...
It's a negation of the "and" set of facts rpresented. two ways to represent that: (.= "and", ^= "or")
(instead of "-L.-O", the negation of which is what you have above, laurels or oaks)
the negation of both of those statements would be: L.O
the second part of the conditional is more straight forward:
whose negation is: -F^-S (or -(F.S))
the contrapositive for the whole would then be:
-F^-S => L.O
If there are not Firs or not Spruces in the park, then there are Laurels and Oaks in the park.
Hope that helped rather than being more confusing.