Hi Sara,
Thanks for the question! This problem as a whole is really interesting, and one of my all-time favorite LR questions. And this sentence that you've asked about is a great one because once you are comfortable with this, it will help you with a host of other conditional statements you will see.
The first thing that presents a problem here is that there is no obvious conditional indicator in this sentence. There's no"if" or "only" or anything similar that would immediately signal that conditionality is present. But, one of the features of conditional reasoning is that it very often deals with absolutes. For example, "all cats are mammals" uses the absolute term "all" (C
M). The same is true for statements such as "every bicycle has wheels" (B
W). Now, those two examples use what I might call "positive absolutes"—"all" and "every" are inclusive of all of the members of the named groups (cats and bicycles).
The same type of idea often applies to negative absolutes, such as "none" or "no." For example, "none of the people at my party wore blue," means that for the group of people at this party, they all had the same characteristic of
not wearing blue (PP
WB). "No" can be used in a similar fashion although I've always thought it's a bit trickier. Let's take a look at how it's used in the sentence in question, "a society that has no laws has no crimes." Let's isolate the laws and crimes part (and we'll just keep in mind that this all refers to the same society). In this case, you have laws and crimes, and then two negatives. At first glance it's hard to tell what's what! But, remember how conditionality works—the sufficient condition, when it occurs, tells you that something else has to occur as well (which is the necessary condition). So, if we have "no laws" does that tell us anything? Yes, it does, it tells us that there are no crimes. Thus, the "has no laws" part is sufficient, and since this refers to the absence of laws, our sufficient condition will be "
L." That means that the remainder is the necessary condition, which is "no crimes," or "
C." The full sentence, when diagrammed, is then:
L C.
This is a tough problem, but it's also a great one to run across early on because it starts you thinking about how conditionality works, the meaning of each type of condition, the importance of indicators, and how conditional reasoning can be present even when no obvious indicator is present. And although right now this looks really challenging, as you encounter more of these types of sentences, you will find that it gets easier and easier to recognize, and that your ability to see the conditionality will improve quickly.
Please let me know if that helps, or if you have any other questions about this. Thanks!