The polynomial-time reduction from sat to csat, as described in section 10.3.3 (p. 452), needs to introduce new variables. the reason is that the obvious manipulation of a boolean expression into an equivalent cnf expression could exponentiate the size of the expression, and therefore could not be polynomial time. suppose we apply this construction to the expression (u+(vw))+x, with the parse implied by the parentheses. suppose also that when we introduce new variables, we use y1, after constructing the corresponding cnf expression, identify one of its clauses from the list below.
note: logical or is represented by +, logical and by juxtaposition, and logical not by -.

Number of megabytes of ram in a computer. qualitative or quantitative? because

1. the program must provide following functions to extract some statistics. note that the data_list parameter specified in these functions may be the same for all functions or different for different functions—that is your choice. a skeleton file is provided on mirmir. a) open_file()prompts the user to enter a year number for the data file. the program will check whether the year is between 1990 and 2015 (both inclusive). if year number is valid, the program will try to open data file with file name ‘year.txt’, where is the year. appropriate error message should be shown if the data file cannot be opened or if the year number is invalid. this function will loop until it receives proper input and successfully opens the file. it returns a file pointer and year. i. hint: use string concatenation to construct the file name b) read_file(fp)has one parameter, a file pointer read. this function returns a list of your choosing containing data you need for other parts of this project. c) find_average(data_list) takes a list of data (of some organization of your choosing) and returns the average salary. the function does not print anything. hints: i. this is not the average of the last column of data. it is not mathematically valid to find an average by finding the average of averages—for example, in this case there are many more in the lowest category than in the highest category. ii. how many wage earners are considered in finding the average (denominator)

I'm taking a class on how to make a movie, and it offers some apps that would be in the process. the thing is, i don't have any of those ha. if you have any tips on some apps i could use, that would be awesome. i don't have an iphone, so don't suggest any apps like imovie. i know that this is a weird question, but it would be super for me. : )