Question 1: Design a DFA with at most 5 states for the language

L₁ = {w {0, 1} | w contains at most one 1 and |w| is odd}.

Provide a state diagram for your DFA.

Approaching the Solution --since we havent really practiced this type of assignment (i.e. had to define our machine based on only having the language given; not the formal 5 tuples), I am providing the steps for how to work through this; you are required to draw the DFA for your answer to this question and provide three test cases (additional instructions for this question are at the end of the explanation below)

To get an idea for the design of the DFA M, it is probably easiest to think about what the strings in L₁ look like. A string w L₁ (i.e. a string (w) that belong to L₁ ) takes on one of the following forms:

w consists of an odd number of 0s and contains no 1s;