Construct an nfa with three states that accepts the language {ab, abc}∗

Sure, here is a step-by-step guide to construct a Non-deterministic Finite Automaton (NFA) that accepts the language {ab, abc}∗:

1. Define the states: We need three states for this NFA. Let's call them q0, q1, and q2.

2. Define the start state: The start state is q0.

3. Define the accepting states: The accepting states are q1 and q2. This is because the language accepts strings that end in either 'b' or 'c', which will be represented by these states.

4. Define the transition function: The transition function δ is defined as follows:

   • δ(q0, a) = q1. This means that if we are in state q0 and the input is 'a', we move to state q1.

   • δ(q1, b) = q2. This means that if we are in state q1 and the input is 'b', we move to state q2.

   • δ(q2, ε) = q0. This means that if we are in state q2 and the input is empty string (ε), we move back to state q0. This allows us to accept multiple instances of 'ab' or 'abc'.

   • δ(q2, c) = q0. This means that if we are in state q2 and the input is 'c', we move back