Let $$w$$ be any string of length $$n$$ in $${\left\{ {0,1} \right\}^ * }$$. Let $$L$$ be the set of all substrings of $$w.$$ What is the minimum number of states in a non-deterministic finite automation that accepts $$L$$?

$$L = {L_1} \cap {L_2}$$ where $${L_1}$$ and $${L_2}$$ are languages defined as follows.
$${L_1} = \left\{ {{a^m}{b^m}\,c\,{a^n}{b^n}\left| {m,n \ge 0} \right.} \right\}$$
$${L_2} = \left\{ {{a^i}{b^i}{c^k}\left| {i,j,k \ge 0} \right.} \right\}$$ Then $$L$$ is

The above $$DFA$$ accepts the set of all strings over $$\left\{ {0,\,\,1} \right\}$$ that

Given below are two finite state automata ($$ \to $$ indicates the start state and $$F$$ indicates a final state)

Which of the following represents the product automation $$ZY$$?