Chapter 12.1, Problem 6TY

To determine

To fill in the blanks of the statement on languages and regular expression.

“ The function that associated a language to each regular expression over an alphabet $\Sigma$ is defined recursively. The base for the definition is the statement that $L(\varnothing )=\_\_\_\_,L\left(\lambda \right)=\_\_\_\_\_,\text{ and }L\left(a\right)=\_\_\_\_$ for every $a$ in $\Sigma$. The recursion for the definition specifies that if $L\left(r\right)$ and $L\left(r\text{'}\right)$ are languages defined by the regular expressions $r\text{ and }r\text{'}$ over $\Sigma$, then $L\left(rr\text{'}\right)=\_\_\_,L\left(r|r\text{'}\right)\text{=\_\_\_ and }L\left(r^{*}\right)=\_\_\_$ ”.