Given S$=\{$ab$,$ cd$\},$ list the first $12$ elements of S$*.$ Remember, Kleene Star includes lambda.

Write a formal grammar that generates all strings over the alphabet $\{0,1\}$ that end in either a $\text{'}0\text{'}$ or a $\text{'}11\text{'}.$

Draw a non$-$deterministic finite automata $($NFA$)$ over the alphabet $\{0,1\}$ that ends in $\text{'}0\text{'}$ or $\text{'}11\text{'}.$

Convert the NFA from problem $3$ into a deterministic finite automata $($DFA$).$ Be sure to show your transition table and draw the resulting machine.

Minimize the below DFA. Be sure to show which states are distinguishable and which are not, as well as draw the resulting minimized machine.