Exercise 7.15 (Independence of an Incompletely Specified Function Regarding Variables). Analyze whether all functions represented by the system function F(x, y) specified in Exercise 7.6 really depend on the variables

(x1, x2, x3, x4, x5, x6, x7). Find all functions described by F(x, y) that depend on the smallest number of variables. Practical tasks:

1 Load the TVL system of Exercise 7.6. This TVL system includes the system function F(x, y) as object number 1.

2 Check whether the system function F(x, y) includes functions that do not depend on one of the variables (x1, x2, x3, x4, x5, x7).

3 Formula (7.65) of [18] allows to analyze the independence of F(x, y)
with regard to a single variable. Generalize this formula for a set of variables. Substantiate this generalization.
4 Check whether the system function F(x, y) includes functions that do not depend on all variables detected in Task 2 of Exercise 7.15.
5 In Task 2 of Exercise 7.15 n variables were found for which the system function F(x, y) includes at least one function that does not depend on one of these variables. Check whether the system function F(x, y)
includes functions that do not depend on n − 1 variables detected in task 2 of Exercise 7.15.
6 Develop a formula that restricts the system function F(x1, x2, y) such that functions depending on more variables than x1 only are excluded.
Substantiate this formula.
7 Calculate all minimal functions described by F(x, y) that do not depend on the sets of variables found in Task 5 of Exercise 7.15 and show the results.