I'm reviewing material for a class I'm retaking before I take it again, and the teacher's homeworks are incredibly cryptic and the class notes aren't very exhaustive. I have a pretty good understanding of DFAs, what I can't understand in this question is the DFA's language:
$$L = \{ w \in \{a, b, c\}^∗ : |w|_a \equiv 2 \pmod{3} \land |w|_b \equiv 2 \pmod{4} \}$$
Really can't understand what kind of accepting state we're looking for here. I'm assuming something to do with the number of of occurrences of a and b in the word w, but not sure about the purpose of mod 3 and mod 4 here. Could it be words of three symbols that have two a's or words of 4 symbols that have 2 b's, hence two accepting states?
No. The equation $a\equiv b\pmod{c}$ means that when $a$ is divided by $c$ the remainder is $b$. Another way of putting it is that there is some integer $k$ such that $a=kc+b$. So the question means that the number of $a$'s is of the form $3+2$ and the number of $b$'s is of the form $4k+2.$