Let $L_1=\{x\},L_2=\{a,b,c\},$ and $L_3=\{y\}.$ Which of the following represents $L_1{L}_3^{***}+L_2?$

a$)\{x,xy,xyy,xyyy,$dots,$a,b,c\}$

b$)\{,x,xy,xyy,xyyy,$dots,$a,b,c\}$

c$)\{,x,xy,xyy,xyyy,$dots,$y,yy,yyy,$dots,$a,b,c\}$

d$)\{xy,xyxy,xyxyxy,$dots,$a,b,c\}$

Consider the language $L$ denoted by $b(ab{)}^{***}aba{b}^{***}?$ Which of the following is true?

a$)$ All strings in $L$ contain at least two $ab\text{'}$s$.$

b$)$ A string in $L$ may contain infinitely many a$\text{'}$s$.$

c$)$ In $L,$ strings have as many $a\text{'}$s as $b\text{'}$s$.$

d$)$ No string in $L$ has just one $ba.$

Consider the machine below. Which of the following is the language accepted by the tachine?

a$)\{\begin{array}{ccc}\text{w}\text{i}\text{n}& \{a,& b{\}}^{***}|w\end{array}$ starts with one $\{$:$b\}$

b$)\{\begin{array}{ccc}\text{w}\text{i}\text{n}& \{a,& b{\}}^{***}|w\end{array}$ contains more a$\text{'}$s than $\{$:$b^{\text{'}}s\}$

c$)\{\begin{array}{ccc}\text{w}\text{i}\text{n}& \{a,& b{\}}^{***}|w\end{array}$ contains more than one $\{$:$b\}$

d$)\{\begin{array}{ccc}\text{w}\text{i}\text{n}& \{a,& b{\}}^{***}|\end{array}$ every $b$ in $w$ is followed by exactly two $\{$:$a^{\text{'}}s\}$