@redstarfish @cnx @shakil_tcs When we say a DFA M "recognizes" a language A, it means M accepts every word in A, and rejects every word not in A.
This means, in your example, M doesn't recognize A1, because it accepts words that aren't in A1 (those from A2 \ A1).
M only recognizes the language C and no other.
This means, in your example, M doesn't recognize A1, because it accepts words that aren't in A1 (those from A2 \ A1).
M only recognizes the language C and no other.
