Please answer Question 2, 3, 4, 5, 6 and 7

Question 2 This question has three parts and tests mathematical induction. (a) Give a recursive definition of the set P of all positive integers greater than 5, (b) formulate the applicable induction principle and (c) hen apply the induction principle to prove that 2n - 3 s 2 for all n> 5. Question 3 Construct a regular expression that defines the language containing all words with exactly one double letter (aa-substring or bb-substring) in them. Question Construct a regular expression that defines the language L (say) containing all the words with either exactly one aba-substring or exactly one bab-substring but not both aba- and bab-substrings. (Hint: For example, the word abab does not belong to L.) Question 5 Build an FA that accepts only those words in which the ab-substring occurs an even number of times and words end in a b-substring. Question 6 Build an FA that accepts the language consisting of only those words that do NOT contain the baa- substring and that do contain an odd number of a's in total. Question 7 Build a TG that accepts the language of all strings that begins with a b and contain at least one aba- I substring or at least one ab-substring or both these strings. Use as few states as possible