an interactive exercise using mouseover script:
Introduction to this self exam:
Examples of technical English on this page consist of stated problems on the themes of set theory and probability. You are not asked to solve the problems, but merely to identify the 2-4 words or phrases in each problem with the most important logical content, by moving your mouse over the words. All words have some minimal logical content, but on this page, you must identify words which describe how a set (or event) is built, or how it is logically related to a probability.

The task cannot be undertaken mechanically, since some English words may have logical content in one part of a sentence, but not in another part of the same sentence. Worse yet, some words with important logical content are implied but unwritten. For example, in the sentence, "A is the set of people who are 18 years old and freshmen, and B is the set of 18-year-old sophomores", only the bolded "and" is used logically, the unbolded "and" could be replaced by a period without changing the logic of the sentence, and the phrase "18-year-old sophomores" means "18 years old and a sophomore" where the bolded "and" has logical content but was originally unwritten.

Sets (and events, which are also sets) are built using 3 logical tools. The tool descriptor is bolded in each case below, but in practice, each bolded word has many synonyms in English.

  • A B is the set of objects, each of which lies in either A or B or both
  • A B is the set of objects,, each of which lies in both A and B,
  • (A complement) is the set of objects not in A

Also, some probabilities are "conditional": in the phrase "the probability of A given that B has occured", that is, P(A|B), the bolded words have important logical content, expressing a relationship between A, B, and a probability. Your task here is to notice both the bolded phrases and their synonyms when used or implied in problems below.:

You may want to review the concept of "conditional probability" in your text.
See a

You may want to review the concept of "conditional probability" in your text. Note that here, one important logical word is "invisible" or unwritten. You may feel this is unfair, but you must find it anyway, since it is needed to solve the problem.
See a

This page last updated
12 January 2011