(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={ww begins with y ends with x} - L3={ww the length of w is at most 4} - L4={w has at least 2 x's and at most 2ys} (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) (8pts) Give state diagrams of DFA's recognizing the following languages. That alphabet is ={x,y} - L5={ww any string that docs not contain the substring xyy} - L6={wwA where A={x,xx,y}}.( denotes all strings in the alphabet) (e) (4pts) Give state diagrams of DFA's recognizing the following L7={ww is not divisible by 6} The alphabet is {0,1}