1. For each of the following languages construct a deterministic finite-state automaton that accepts the language (No dead state).

a. { 1z | z = 3x + 5y for some natural numbers x and y }

b. { x | x is in {a, b}*, and x contains an even number of a's and an even number of b's }

c. { x | x is in {0, 1}*, and the number of 1's between every two 0's in x is even }

d. { x | x is in {0, 1}*, and the number of 1's between every two substrings of the form 00 in x is even }