I hope the holiday season is treating you all very well. Make sure to wear layers, and eat your vitamins because the flu is floating around. The last thing you want is to catch a cold right during your LSAT prep. Seeing as we are a little over a month away from the February LSAT, I thought we could have a little Sufficient & Necessary refresher.
First thing’s first. Let’s have a quick overview of the basics. The left-hand side of the arrow is the sufficient condition. The right-hand side of the formula is the necessary condition. The existence of the sufficient condition proves the existence of the necessary condition. Each Sufficient & Necessary sentence has a contrapositive. To make a contrapositive, all you have to do is reverse the variables and negate. Don’t just reverse! Don't just negate! Reverse and negate!
Let’s go over some examples:
(1) Santa only lives in the North Pole
S ==> NP
not NP ==> not S
Easy, right? So we have the possibility that someone lives in the North Pole, but is not Santa. It could be an elf, or Mrs. Claus! Let’s get a little more complicated.
(2) The only person that lives in the North Pole is Santa.
NP ==> S
not S ==> not NP
“The only” seems to trip up many LSAT studiers. You cannot treat “only” and “the only” as the same. “Only” introduces a necessary condition, whereas “the only” introduces a sufficient condition. In this situation we have the possibility that Santa doesn’t live in the North Pole. He could, in this case, decide to move to somewhere more tropical and work on his tan.
(3) Eggnog has both nutmeg and bourbon in it.
E ==> N & B
not N or not B ==> not E
Remember to always switch an “and” to an “or,” and vice versa.