2. Write regular expressions for the following character sets, or give reasons why no regular expression can be written a. All strings of lowercase letters that begin and end in a; b. All strings of digits that contain no leading zeros; c. All strings of digits such that all the 2's occur before all the 9's. d. All strings of a's and b's that contain exactly as many a's as b's. (Optional) All strings of a's and b's that contain an odd number of a's or an odd number of b's (or both)