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Not sure what this operation does, which is why i'm on here. It's not the cartesian product and no idea what it's called. I need to know to prove:

For any language L, (Null set)L = L(null set) = (null set)


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up vote 1 down vote accepted

This is only a guess. $$ AB = \{ a \circ b \,:\, a \in A, b \in B\}, $$ where $\circ$ denotes concatenation. For example, $$ \{ a, b \} \{ ce, dk \} = \{ ace, adk, bce, bdk \}. $$

When $A$ is the null set, the quantity $AB$ is also a null set, because every string in $AB$ is supposed to be of the form $ab$ where $a \in A$ and $b \in B$. But the null set contains no strings, by definition; so $ab \in AB$ is not possible. (You can similarly argue that if $B$ is the emptyset, then $AB$ is again empty.)

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That seems correct, and thank you for giving me the name of the operation :) – oorosco Sep 16 '11 at 6:32

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