Draw DFAs for each of the languages below. None of your DFAs may contain more than $4$ states. $(10$ points$)$

a$)$ All strings over $\{0,1\}$ that contain an even number of $1s.$

b$)$ All strings over $\{0,1\}$ where the number of $0$ s and $1s$ are both even.

Draw NFAs for each language in question $1.(5$ points$)$

Which languages in question $1$ accept these strings? Show the work. $(10$ points$)$

a$.101010$

b$.110011$

c$.010101$

d$.001100$

e$.000111$Example to show the work:

String Acceptance

String: $000001$ :

DFA $($a$)$: Even number of $1s$

Start at q$0.$

Read $0$: Stay at q$0.$

Read $0$: Stay at q$0.$

Read $0$: Stay at q$0.$

Read $0$: Stay at q$0.$

Read $0$: Stay at q$0.$

Read $1$: Stay at q$1.$

End at q$1.$ Result: Not accepted as you are at q$1,$ that is not accepting state.