LSAT Conditional Reasoning: Diagramming "Unless"

[Jon Denning]

A student of ours using the Logic Games Bible asked me the following question about a diagramming drill recently:

"For the example with rule, 'G does not speak fourth unless Q speaks second,' I originally entered G4 with a slash
(/) to indicate the not. However the answer key shows no slash. Please explain!"

Since I know that "unless" statements like the one in question are a common source of difficulty for people, I want to share my reply here in hopes that anyone else facing similar issues can get them resolved.

My response:

The example you cite is an interesting one, because it uses one of four special conditional indicator words: “unless.” (The other three are “until,” “except,” and “without,” as we’ll see)

Those four words have the rather unique property of implied negation or exception or absence when used. Consider: if you are “without” something, you’re missing it; ditto “except” (the exception, so everything but that outlier), “until” (the time before something occurs), and “unless” (the one circumstance that avoids the general rule; again, the exception).

Put another way, a word like “unless” provides you with a scenario where something WON’T occur. “I’m going to the concert tonight UNLESS it’s raining.” That means there’s only one way I won’t go: rain. So if I don’t go to the concert we know something! It must be raining. How would we diagram that idea?

No Concert Rain

Note though that the idea in the original sentence—“I’m going to the concert”—has been negated, “I’m NOT going to the concert.” The word unless creates that negation. Except, until, and without do too. And that’s what you’re missing in your diagram below, as I’ll explain!

There’s a really simple technique you can use when you see one of those four words called The Unless Equation. It’s two quick steps and it works every time:

1. Whatever word or idea unless modifies becomes necessary (it goes at the end of the arrow). So above
we see “...unless it’s raining.” That makes “Rain” the necessary condition, Rain.

2. Whatever is left gets negated and becomes sufficient (beginning of the arrow). The negative nature of
unless gets applied to the other term(s) and it starts the chain. Above, originally we had “I’m going to the
concert tonight...,” so that gets negated to “No Concert” and is in front of the arrow, No Concert

Together then we have: No Concert Rain. And the contrapositive where we flip the terms and make each one exactly opposite: No Rain Concert.

Apply that to your example below:

1. Unless describes “Q in 2,” so that’s necessary: Q2

2. The rest is “G not 4,” so we negate that to “G is in 4,” and it becomes sufficient: G4

Put them together to get G4 Q2, and the contrapositive Q NOT 2 G NOT 4 (we’d show those with slashes on the test).

As you can probably imagine, this causes confusion for a lot of people at first (it’s a weird idea until someone walks you through it), so we’ve written a lot about it. Check out the following links if you’d like to read more:

http://blog.powerscore.com/lsat/bid/281 ... s-Equation

http://blog.powerscore.com/lsat/powersc ... the-day-15 (this will take you to our LSAT
Forum where we’ve discussed the ideas above at great length, as well)

http://blog.powerscore.com/lsat/bid/293 ... n-the-lsat

http://blog.powerscore.com/lsat/beyond- ... n-the-lsat (this one is a little more advanced)


So that’s how to handle unless-type words when you see them on the test, whether in LG or LR! With a little practice you’ll find these become second-nature and entirely straightforward.

I hope this helps!

[Mmjd12]

Hi there,

A question regarding the Unless Equation with a statement that has multiple necessary conditions:

If there are two or more necessary conditions in a statement, are they always grouped together by “and”? Can there be an “or”? And if so, how do you tell the difference?

In other words, are multiple necessary conditions always triggered together? I’m sure there are exceptions to this, but I would have a hard time deciphering the difference, I think.

For example,

One should not intentionally misrepresent another person’s beliefs unless one’s purpose in doing so is to act in the interest of that other person, with their permission.

I would diagram this as:

Intentionally misrepresent belief act in their best interest + with their permission


But I could see how it could be diagrammed as:

Intentionally misrepresent belief act in their best interest OR with their permission


Are necessary conditions always triggered to together? If not, how can you tell if the sufficient clause is enough to trigger one but not all the necessary conditions?

Thanks so much,

[Jeff Wren]

Hi Mmjd12,

First, the rule about multiple necessary conditions is the same whether you are using "unless" or any other conditional indicator. In other words, multiple necessary conditions are treated the same in any conditional statement.

For any conditional statement with multiple necessary conditions, they will either be linked with "and" or with "or" based on the meaning of the original sentence in English.

In some cases, the sentence will convey that each of the necessary terms must occur, which would be diagrammed "and" or with a "+" in our notation.

For example, "If it rains, then I will stay home and watch TV." Both of those are necessary and would be linked with a "+" sign.

In other cases, the sentence will convey that at least one of the necessary terms must occur, which would be diagrammed "or" in our notation.

For example, "If it rains, then I will watch TV or take a nap." Here, only one of those necessary terms must occur to satisfy the conditional statement.

While I used "if/then" in the examples above for simplicity, the same applies with "unless."

Now, in your example, you didn't use the word "and" or use the word "or." One option would be to just diagram the necessary as one long term "one’s purpose in doing so is to act in the interest of that other person, with their permission." In this case, if any part of the necessary fails, then the sufficient condition does not occur.

If you do want to separate it out, then I'd use the word "and" here because the wording of the sentence conveys that both "act in the interest of that other person" and "with their permission" are necessary. In order to diagram "or," the word "or" must appear in the sentence or some other clarification that at least one (rather than both) of the necessary terms must occur.