Why is $\emptyset L = L\emptyset = \emptyset$ correct?
$L_1L_2$ means the set of all strings you can make by choosing one from&nbsp;$L_1$ and one from&nbsp;$L_2$ and concatenating the two strings.  So how many ways can you choose a string from the empty set of strings and one from&nbsp;$L$?  None at all! So there are no such concatenations and $\emptyset L = \emptyset$.

The key point is that $\emptyset$ is the language that contains no strings at all. The empty string is a string (it's the string with no letters at all) so the empty string is not a member of the empty language: $\{\epsilon\}\neq\emptyset$.