Final answer:
L1 consists of strings of the letter 'x' where two 'x's can be prepended to any existing string in the set. It can be described by the regular expression x* (including zero occurrences of 'x') or x+ (if excluding the empty string).
Step-by-step explanation:
The student is asking about the structure of a particular set known as L1. According to Rule 1, x is in L1. Rule 2 specifies that if w is any word in L1, then xxw is also in L1. The description provided outlines the beginning of what can be considered a formal language in automata theory or formal language theory, with a recursive definition.
With this given information, the structure of L1 can be determined. Rule 1 is the base case which declares that the word x is in the language. Rule 2 is the recursive definition that allows for building longer words by prepending two x's to any word w already in L1.
Therefore, the set L1 would consist of strings like x, xxx, xxxxx, and so on, where each string is formed by adding two x's to the front of the previous string in the set. This set is equivalent to the regular expression x* (or x+ if we assume that the empty string is not part of L1). This represents languages containing any number of x's (including zero, which is represented by the empty string in the case of x*).