(a) (12pts) Give state diagrams of DFA's recognizing the following languages. The alphabet is {x,y}. = L1 = {ww has length 5 and its third symbol is a x} . L2 {wl w begins with y ends with x} L3= {ww the length of w is at most 1} L4 = {w has at least 2 x's and at most 2 y's} (b) (4pts) Write the formal definition of L2 (c) (4pts) Construct a DFA that accepts strings over alphabet {x, y, z} whose symbols are in alphabetical order (for example: xxyzz, yz and xzz are accepted but not xzy or xyzx). (d) (&pts) Give state diagrams of DFA's recognizing the following languages. That alphabet is = {x,y} L5 {w w any string that does not contain the substring myy} L6 = {w W E A where A = * {2, XZ,y}}. (S* denotes all strings in the alphabet) (e) (4pts) Give state diagrams of DFA's recognizing the following L7 = {w w is not divisible by 6} The alphabet is {0,1}