am really stock on those - i will apreaciate the help

- Problem 2. Give state diagrams of DFA recognizing the following languages. In all cases the alphabet is {0,1} (1) {ww contains at least three 1s} (2) {ww does not contain substring 110} - Problem 3. A number is a prime if it cannot be a product of two numbers less than it. For examples, 2,3,5,7,11,13 are prime numbers, but 6,8,10 are not. (1) Prove by contradiction that there are infinite prime numbers. Hint: Assume that there are only finite prime numbers p1,p2,,pk. Think about the number p1p2pk+1 (2) Show that the proof by contradiction can be revised to derive an algorithm to find the (k+1)-th least prime number pk+1 given input of the first k least prime numbers p1,,pk. (3) A twin number is a pair of prime numbers of difference 2. For examples, (3,5), (11, 13), and (29,31) are all twin numbers. Search internet about twin number conjecture. Provide its history and current research status