1. A set S contains n elements. How many possible subsets can be formed from S(including Sand the empty set)? (Hint: you might want to try a set with n= 0 elements and count the total number of subsets that could be formed. Then try n= 1,n= 2,n= 3 until you see a pattern start to develop.)

2. Let be an alphabet. Consider strings u,v,w. Prove that the concatenation operation is associative (i.e. (uv)w=u(vw)).

3.Let ={0,1}be an alphabet. Now consider/interpret as the set of all possible realnumbersRcontained on the interval [0,1] represented in base 2. LetLbe the language defined by the set of strings contained in Q(the set of rational numbers). Given a string in, describe an algorithm that will determine ifL(i.e. describe an procedure to either accept or reject ).