Theory of Computation - Automata Theory

A regular language L is accepted by a non-deterministic finite automaton (NFA) with n states. Which of the following statement(s) is/are FALSE?

Consider the following deterministic finite automaton (DFA) defined over the alphabet, $\Sigma = \{a, b\}$. Identify which of the following language(s) is/are accepted by the given DFA.

Let Σ = {1,2,3,4}. For x ∈ Σ*, let prod(x) be the product of symbols in x modulo 7. We take prod(ε) = 1, where ε is the null string. For example, prod(124) = (1 × 2 × 4) mod 7 = 1. Define L = {x ∈ Σ* | prod(x) = 2}. The...

Let δ denote the transition function and $\hat{\delta}$ denote the extended transition function of the $\epsilon$-NFA whose transition table is given below: Then $\hat{\delta}(q_2, aba)$ is