1. A set S contains n elements. How many possible subsets can be formed from S (including S and 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 S = {a,b}. Let u = abab3 and v = bab be strings in L. Compute the following (a) uv and uvl. (b) vu and (uul. (C) eu. (d) veu. (e) uev. 3. Let S be an alphabet. For any strings u,v e , prove that (a) uv = ]u[ + ul. (b) uv= vul