# What is this operation between sets {a, b}{c, d} do?

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)

Thanks

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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.)