$(1)$ Consider the NFA N:

iv

Compute the $-$closure of each state.

Construct an NFA Nne without $-$transitions such that $N$~$=N$ ne$.$

Construct a DFA M that is equivalent to Nne.

Design DFAs for the following languages:

$($w starts with $0$ and has even length$)$ or $($starts with $1$ and has odd length$)\}$

every odd position of $w$ is a $1$