University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Logic"
Read Definition 5 up to and including example 8 on pages Lo-13 and Lo-14. This reading also applies to the topic for Subunit 2.1.2 of this course. This reading gives important examples of using logic to represent statements in mathematics. As you read this text, please keep in mind that formal language includes logic, binary functions, sets, and programming languages. Informal language includes English and other natural languages.
In our study of logic, our primary interest is translating between logic and English (or natural languages). In addition, you will find it useful to translate between informal (that is, natural) languages. For example, suppose you have an English statement that you find difficult to translate to logic. Rewriting or translating the statement to an equivalent English statement usually makes the translation to logic easy. Translating between informal or natural languages also occurs when we translate from one natural language to another, for example, from English to Spanish.