Construct a regular expression defining each of the following languages over the alphabet = {a,b}.

a) All words in which a appears tripled, if at all. This means that every clump of a's contains 3 or 6 or 9 or 12, etc. a's. b) All words that contain at least one of the strings S₁, S₂, S₃, or S₄. c) All words that contain exactly 2 b's or exactly 3 b's. d) All strings that end in a double letter. A double letter means the same letter repeated twice - i.e., aa or bb. e) All strings that do not end in a double letter. f) All strings that have exactly 1 occurrence of a double letter in them. g) All strings in which the letter b is never tripled. This means no word contains the substring bbb. h) All words in which a is tripled or b is tripled, but not both.