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

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

Note: $\emptyset^∗ =\{\epsilon\}$.

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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.

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