3. Let S be an alphabet. For any strings u, v E , prove that (a) |uv= |u[ + ]ul. (b) |uv= |vul. 4. Let I be an alphabet. Consider strings u, v, W 2. Prove that the concatenation operation is associative (i.e. (uvw = u(vw)). 5. Let S = {a,b}. Write out three representative strings for each of the following language definitions (a) L = {a" bm >0} (b) L = {a"b" |m > 0, n >0} (C) L = {bab"|m>0,n0} (d) L = {(ab)|m >0} (e) L = {a3b"a*|m >0}