Consider a DFA A given in tabular form as follows: 291 92 Note that the inputs to A are binary strings (a) Draw the transition diagram for A (b) True or false: The number of leading zeroes in an input string makes no difference in whether A accepts the string or not. (c) Write the numbers 0,1,2,... , 10 in binary, and feed each of the binary strings into A For each number, say which state A is in after reading the string and whether A accepts the string. (d) Let be the extended transition function of A. Prove the following: For any binary string w representing a natural number n, (q0,w)-qr, where r is the remainder of n divided by 3. [Hint: Use simple induction on |w]. Note that if w represents n in binary, then w0 represents 2n, and w1 represents 2n + 1 . (By convention, e represents zero in binary.)] (e) Use the statement above to conclude that the language of A is the set of all binar;y representations of multiples of 3