1. Draw a DFA transition diagram for binary strings which - a. do not start with 101 b. contain exactly two 1s c. contain at most two 1s d. contain at least two 1s Convert your DFA to RE using the state elimination method 2. Try to prove the followings using algebraic laws of RE [arises while converting DFA to RE]: a. (0/1+0)1+01(0/1)=(0/1)101(0/1) b. 10(0/1+0)=10/10(0/1)0.