Welcome to our ongoing series on the more nefarious elements of diagramming.
Topping the agenda today are “unless” questions. These are much more straightforward than the “only” conditionals we reviewed last week. Unlike “only” questions, which require one to search for the referent, “unless” questions have a more standardized approach. Consider the following:
“Unless I just brushed my teeth, you’ll find me sipping a cold glass of orange juice”
What does this mean? It tells us that, in all cases where I haven’t just finished brushing my teeth, I’ve got a tall glass of nature’s goodness by my side. To simplify: if I have not just brushed, then I’ve got OJ. Look diagrammable?
Sure does. We have our best two indicators — if and then — followed by a clear sufficient and necessary condition. Our conditional diagram should look something like:
not JB —> OJ
And if we take the contrapositive? Flip it, negate each side, and we have:
not OJ —> JB
Since I am without OJ, we know — on the basis of the original conditional — that I must have just brushed. As such, we see that the term “unless” introduces the necessary condition.
This example illustrates a nice little maneuver. “Unless,” in terms of logical structure, equates to “if not.” Meaning that “unless I just brushed my teeth,” “unless the sky falls,” and “unless my watch is incorrect,” equates to “if it is not the case that I just brushed my teeth,” “if it is not the case that the sky falls,” and “if it is not the case that my watch is incorrect,” respectively.
One more example to drive it home.
“Unless I finish my LSAT homework, I won’t go out tonight”
To solve this self-serving example, just slap an “if not” in place of the “unless” as we practiced. Your diagram becomes:
not FLH —> not GOT
The contrapositive being, “if I go out tonight, then I must have finished my LSAT homework.” Your contrapositive diagram should look like this:
GOT —> FLH
I have one further tidbit of excellent news. This same “if not” rule applies to “until,” “without,” and “except,” as well. Meaning that “until I find a spoon I can’t eat my soup” equates to “if it’s not the case that I find a spoon, then I can’t eat my soup.” You’ll see these questions popping up quite frequently in your LSAT studies and on the test, so it’s a key skill to master.
The take away for this week is that, if you see “until,” “unless,” “except,” or “without” embedded in your LR question, then you’ve encountered a necessary condition. The most efficacious way to diagram these statements is to simply swap the “unless” for an “if not,” and diagram that negation. Unless you forget this method, you’re 180 bound.