Hand-drawn diagrams for problems 1-2 are acceptable.

1. For each of the languages A and B given below, show a state diagram of a deterministic finite state automaton (DFA) that reconizes the language. The alphabet of the two languages is {a, b}. A={x | x (a+b)* contains 2n+3 as for n 0} B={x | x (a+b)* contains 3n+1 bs for n 0}

2. Show a state diagram of a DFA that recognizes the intersection of the two languages given in problem 1.