Problem 1. (20 points) Give regular expressions for the following languages. Provide brief justifications for parts c and d (you do not need to give a detailed proof). a. The set of binary strings that contain the substring 0101. b. The set of binary strings that contain at least three l's. c. The set of binary strings in which the number of l's is divisible by 3. d. The set of nonempty strings over the alphabet {0,1,2,3) such that the last digit does not appear earlier in the string