1. Give a regular expression for each of the following languages. (10 points) a. The set of binary strings not containing consecutive 1's. b. The set of binary strings containing exactly one instance of 11 somewhere inside. C. The set of binary strings with at most one pair of consecutive 1's ie, if 11 is present, it can occur exactly once. d. The set of binary strings containing at least two zeros somewhere. e. The set of binary strings containing at least two consecutive zeros and ends with 1. 2. Let R, S and T be any three regular expressions. Prove True or False for the following. (5 points) a. ( + RS = R* s b. (R+S4* S* = (R* s)* (6 points) 3. Use Pumping Lemma to prove these languages are not regular. a. {0" 10" | n 1} b. {on 1m | n sm} 4. Provide the proof for these theorems. a. If Land M are regular languages, then so is LU M. (4 points) Note: Submit your answers to Canvas. No hard copies