We defined the operation of concatenation for sets of strings on p. 10,

ab = { xy | x \in a and y \in b }

are the regular sets closed under concatenation? that is, if a and b are regular sets, is ab guaranteed to be a regular set? prove or show a counterexample.

Computer security/cybersecurity1) each of the following code fragments contains a number of security vulnerabilities. for each fragment, identify these security vulnerabilities and, for each vulnerability, discuss at least one way that it could be improved. note that in your discussion of how each vulnerability could be improved, you do not need to re-write a new version of the program in c; simply discuss your solution, either in pseudocode or in 1-2 sentences. a) /* file descriptor leak */#include #include int main(int argc, char *argv[]){ char *filepath = argv[0]; char *shellpath = argv[1]; file *passwords; passwords = fopen(filepath, "r"); /* read the password and do something with it */ /* . . */ /* fork and execute alternative shell */ execl(shellpath, "shell", null); }b)#include /* assume the following function is written for an electronic storefront. the user will enter the id of the item to be ordered, as well as the quantity of units that they would like to purchase. the program will then lookup the price for the price for the item using a predefined function, and return the total cost of the order.*/int gettotalcost(){ char itemid[9]; int price, unitsordered, cost; printf(" enter the 9-digit id of the item to be ordered: "); scanf("%s", & itemid); /* lookup the price according to the itemid */ price = getpricebyid(itemid); printf(" enter the quantity of units to be ordered: "); scanf("%d", & unitsordered); cost = price * unitsordered; return cost; }c)#include /* the following function is intended to return a user's full name by concatenating the user's first and last name into a single string and then returning that string. */char *getfullname(char *firstname, char *lastname, int max_len){ char fullname[max_len]; strcpy(fullname, firstname); strcat(fullname, " "); strcat(fullname, lastname); return fullname; }d)#include /* the following code snippet runs through the list of cli arguments entered and displays them to the console. */int main(int argc, char *argv[]){ int i; printf("you've entered the following arguments: "); for(i = 0; i < argc; i++){ print(argv[i]); printf("\n"); } /* */}