Q$1(3$ points$)$

Give a nondeterministic finite automata to accept each of the following languages:

a$)(1\mathrm{.}5$ point$)$ Let the alphabet be $\backslash (\backslash \{$a$,$ b$,$ c$,$ d$\backslash \}\backslash ).$ The set of strings such that the final symbol has not appeared before.

b$)(1\mathrm{.}5$ points$)$ Let the alphabet be $\backslash (\backslash \{0,1\backslash \}\backslash ).$ The set of strings such that there are two $1\text{'}$s separated by a number of positions that is a multiple of $5.$ Note that $11$ is also a member of the language where two $1\text{'}$s are separated by $0$ positions, which is the $0$ multiple of $5.$

Q$2(2$ points$)$

Convert the following NFA to a DFA. Show all your steps.