# Find the number of strings in the language $(∅∅^∗ + ∅)$

Consider the language $$L = \emptyset\emptyset^∗ + \emptyset$$.

How many words does $$L$$ contain? Zero or one?

Note: $$\emptyset^∗ =\{\epsilon\}$$.

Your language could be simplified as follows, using $$\emptyset^* =\{\epsilon\}$$:
\begin{align*} L(\emptyset\emptyset^*+\emptyset) &=L( \emptyset . \{\epsilon\} + \emptyset) \\ &=L(\emptyset +\emptyset) & (\emptyset.\{\epsilon\}=\emptyset) \\ &=L(\emptyset) & (\emptyset + \emptyset = \emptyset) \end{align*}
So the language L accepts empty language which is $$L =\{ \}$$, which means that it contains zero elements.
Please be aware that the empty language is different from language consisting of the empty string, which is $$L =\{\epsilon\}$$, and which contains the element $$\epsilon$$, while the empty language contains zero elements.