questions 2-6

Question 2 This question has three parts and tests mathematical induction. (b) formulate the applicable induction principle and Give a recursive definition of the set P of all positive integers greater than 5 (c) then apply the induction principle to prove that 2n-3s 2-2 for all n>5 Question 3 that defines the language containing all words with exactly one double Construct a regular expression letter (aa-substring or bb-substring) in them. Question 4 Construct a regular expression that defines the language L (say) containing all the words with either 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 Question 3 Construct a regular expression that defines the language letter (aa-substring or bb-substring) in them. containing all words with exactly one double Question 4 a rani ilar Anreesinn that defines the lanalIA A I Annlaininn all