Hello, I need help with the entire question from a) to e). Thank you!

(a) Write the negation of the following: [3] [3] [6] -9 VxP(x) VQ(2) (b) Each student has a password, which is 5 characters long and each character is either a digit or a lowercase letter. Each password must start with a lowercase letter and contain at least TWO digits. How many possible passwords are there? (c) Using the Master theorem write the time complexity of the following T(n) = 8T(n/2) + O(n") T() = 9TR/3)+2(m) (d) Design a context-free grammar that accepts all binary words ending in letter 0. [4] [3] (e) Give a finite automaton that accepts all binary words that contain exactly one occurrence of 00. (Note that 100010 does not meet this criterion because 000 contains two 00's.) [7] (a) Write the negation of the following: [3] [3] [6] -9 VxP(x) VQ(2) (b) Each student has a password, which is 5 characters long and each character is either a digit or a lowercase letter. Each password must start with a lowercase letter and contain at least TWO digits. How many possible passwords are there? (c) Using the Master theorem write the time complexity of the following T(n) = 8T(n/2) + O(n") T() = 9TR/3)+2(m) (d) Design a context-free grammar that accepts all binary words ending in letter 0. [4] [3] (e) Give a finite automaton that accepts all binary words that contain exactly one occurrence of 00. (Note that 100010 does not meet this criterion because 000 contains two 00's.) [7]