For each problem, the alphabet will be { = {0, 1, 2} and we will be considering each string to be an integer base 3. For the DFA design problems, draw the state diagram in JFLAP, export the image as a png or jpg file, and include it as part of your submission. (a) Design a DFA that recognizes the language: {W {0,1,2}* | w in base 3 is congruent to 0 mod 2.} (Note: this set does include the empty string.) (b) Design a regular expression that describes the language: {W {0,1,2}* | w in base 3 is congruent to 0 mod 2.} (Note: this set does include the empty string.) (c) Design a DFA that recognizes the language: {we {0, 1, 2}* | w in base 3 is congruent to 1 mod 4.} (Note: this set does not include the empty string.) (d) * Design a regular expression that describes the language: {W E {0, 1, 2}* | w in base 3 is congruent to 1 mod 4.} (Note: this set does not include the empty string.)