1) Design an NFA with no more than $5$ states for: $$L_1 = \left \{aba b^n \mid n \geq 0 \right \} \cup \left \{ ab a^n \mid n\geq 0 \right \}$$
2) Design an NFA with $3$ states for: $$L_2= \left \{a^n \mid n \geq 1 \right\} \cup \left \{ b^m a^k \mid m,k \geq 0\right \}$$
3) Design an NFA with $4$ states for: $$L_3= \left \{ a^n \mid n\geq 0 \right \} \cup \left \{b^n a \mid n \geq 1 \right \}$$