By Nathan Fox
Yesterday, I offered a definition of the word “assumption” using a very simplistic mathematical example. Today, I’m going to dig a bit deeper into the Assumption category by using another super-simple bit of math. Don’t panic! If you passed third grade, you’ve seen this math before.
Many students struggle with assumption questions because they don’t understand that there are two very different types of assumptions. The purpose of this post is to start teaching you the difference.
The previous post offered an example of an assumption that was both sufficient and necessary. Today I am going to talk about just one of those types, the “Sufficient Assumption.” So consider the following argument:
Premise: Anything times zero equals zero. Conclusion: Therefore A times B equals zero.
Question: “Which one of the following, if true, would allow the conclusion to be properly inferred?” Or, stated another way, “Which one of the following, if assumed, would justify the argument’s conclusion?” Both of these are asking for sufficient assumptions. (You might want to memorize the wording of those questions, so that you can differentiate a sufficient assumption question from a necessary assumption question.)
This question is asking you to prove the argument’s conclusion. In order to prove a conclusion on the LSAT, the conclusion of the argument must be connected, with no gaps, to the evidence offered. So we need an answer that connects the evidence “anything times zero is zero” to the conclusion “A times B is zero.”
It’s pretty simple. The answer must contain one of the following:
“A equals zero.” If it’s true that A is zero, and if it’s true that anything times zero equals zero, then no matter what B is, the conclusion “A times B equals zero” would be proven correct. And proof is what we’re looking for on a sufficient assumption question.
“B equals 0″ would be just as good, because no matter what A is, the conclusion “A times B equals zero” would be proven correct.
Here’s the really interesting part (if you’re a nerd like me, which I hope you are). While “A equals zero” and “B equals zero” are each sufficient to prove the conclusion correct, neither of these statements, independently, are necessary in order for the argument to possibly make sense. A could be 1,000,000, and the conclusion “A times B equals zero” could still be conceivable (if B equals zero). Likewise, B could be 1,000,000 and the conclusion could still be possible (as long as A equals zero.) So if the question had said “which one of the following is an assumption required by the argument,” (that’s asking for a necessary component of the argument) then “A equals zero” would not be a good answer. Nor would “B equals zero.”
The definition of “sufficient assumption” is “something that would prove the argument’s conclusion to be correct.” Go ahead and memorize that. I’ll be back soon to offer a definition of “necessary assumption.” Once I’m done with that, I promise I won’t use any math for a while.