Show that the class P, viewed as a set of languages, is closed under union, inter- section, concatenation, complement, and Kleene star. That is, if L1,L2 ∈ P, then L1 ∪ L2 ∈ P, etc.

Data is processed, stored, and transmitted as a series of 1s and 0s. each 1 or 0 is called a(n) . a series of eight 0s and 1s, called a(n) , represents one character—a letter, number, or punctuation mark. data becomes when it is presented in a format that people can understand and use. digital signals are represented by two different , such as +5 volts and +.2 volts. digital data can also take the form of light and dark spots etched onto the surface of a cd or the positive and negative orientation of particles on the surface of a hard disk. data consists of numbers that might be used in arithmetic operations. it can be represented digitally using the number system. data is composed of letters, symbols, and numerals that are not used in arithmetic operations. computers represent this type of data using , ebcdic, unicode, or utf-8. data is quantified using terms such as or kibibyte (1024 bytes), and prefixes such as or mebi (1,048,576), and giga or (1,073,741,824). to reduce file size and transmission times, digital data can be compressed. compression provides the means to compress data and reconstitute it into its original state. compression throws away some of the original data during the compression process. compressed files usually have at the end of the file name and are represented with special icons. these files have to be or unzipped before you can view the data they contain.

What can tanya do now to start preparing for the college and scholarship application process? think about her grades, activities in which she can get involved, possible part-time jobs at which she can work, and standardized tests she can take. (10 points) apex

What is a costume plot? why is it important to a film or theater production?