For each of the statements below, state whether it is true or false and then prove your answer.

(a) 15n 3 log n + 10n 2 + 50 is O(n 3 log n).

(b) 3n 2 − 12n + 2 is Ω(n 3 )

(c) 2n+1 is Θ(2n )

(d) 22n is O(2n )

(e) log(n!) is O(n log n) (Hint: compare n! and n n )

Print "censored" if userinput contains the word "darn", else print userinput. end with newline. ex: if userinput is "that darn cat.", then output is: censoredex: if userinput is "dang, that was scary! ", then output is: dang, that was scary! note: if the submitted code has an out-of-range access, the system will stop running the code after a few seconds, and report "program end never reached." the system doesn't print the test case that caused the reported message.#include #include using namespace std; int main() {string userinput; getline(cin, userinput); int ispresent = userinput.find("darn"); if (ispresent > 0){cout < < "censored" < < endl; /* your solution goes here */return 0; }