1. (30 Points) L1={ww has exactly two a's } and L2={ww has at least 2 b's }, In L1 and L2,={a,b}. (a) (20 Points) Build a deterministic finite state machine for L1. (b) (20 Points) Build a deterministic finite state machine for L2. (c) (30 Points) Build a deterministic finite state machine for L1L2. (d)(30 Points) Minimize the deterministic finite state machine constructed in (c). Show the work using the equivalence class. You also need to show the work even the DFSM you built in (c) is already a minimal deterministic finite state machine