91Ó°ÊÓ

Let \(\Sigma\) be an alphabet. Define \(\Sigma^{*}\) recursively. (Hint: use concatenation.)

\(n\) denotes a positive integer less than \(10 .\) Rewrite each set using the listing method. \(\\{n | n \text { is divisible by } 3\\}\)

In Exercises \(34-37, n\) denotes a positive integer less than \(10 .\) Rewrite each set using the listing method. \(\\{n | n \text { is divisible by } 3\\}\)

Let \(A=\\{\mathrm{b}, \mathrm{c}\\}, B=\\{\mathrm{x}\\},\) and \(C=\\{\mathrm{x}, \mathrm{z}\\} .\) Find each set. $$A \times(B \cup C)$$

According to a survey among 160 college students, 95 students take a course in English, 72 take a course in French, 67 take a course in German, 35 take a course in English and in French, 37 take a course in French and in German, 40 take a course in German and in English, and 25 take a course in all three languages. Find the number of students in the survey who take a course in: English and French, but not German.

\(n\) denotes a positive integer less than \(10 .\) Rewrite each set using the listing method. \(\\{n | n \text { is divisible by } 2 \text { and } 3\\}\)

According to a survey among 160 college students, 95 students take a course in English, 72 take a course in French, 67 take a course in German, 35 take a course in English and in French, 37 take a course in French and in German, 40 take a course in German and in English, and 25 take a course in all three languages. Find the number of students in the survey who take a course in: English, but neither French nor German.

In Exercises \(34-37, n\) denotes a positive integer less than \(10 .\) Rewrite each set using the listing method. \(\\{n | n \text { is divisible by } 2 \text { and } 3\\}\)

Mark each as true or false, where \(A, B,\) and \(C\) are arbitrary sets and \(U\) the universal set. $$A \subseteq A \cup B$$

Define the language \(L\) of all binary representations of nonnegative integers recursively.