Game: Set Match

Consider the word walruses and the phrase cheerful walruses. The diagram below shows one way to illustrate the relationship between these phrases.

Each circle stands for the set of things that could be described by the relevant word or phrase. Since all cheerful walruses are walruses, the region for cheerful walruses is fully contained inside the region for walruses. The sizes of the circles are irrelevant; what matters is how they overlap and which ones are contained inside others.

This example relates to an important question: how does the meaning of a phrase relate to the meanings of the words that make it up? This question comes up in computational linguistics because computers that process language must be able to determine the meanings of complex phrases.

Note that this problem only gives a partial picture of meaning in language. Some nuances that are left out are important in linguistic theories, but for the sake of this problem you should only use the information presented.

Below are 18 words and phrases in arbitrary order, along with a diagram representing their meanings.

Notes. Alleged spies are people who have been accused of being spies but who may or may not actually be spies. The phrase small big elephants may be confusing without context; here is an example where it can occur: “That’s a big elephant, but compared to other big elephants it’s relatively small; it’s a small big elephant.” We assume that cars cannot be both green and purple at the same time. We use the informal definition of berry, in which strawberries are a type of berry. We assume that elephants cannot be spies.