Post-concatenation of the languages represented by the null set

Question

I have a small question regarding concatenation of regular languages:

Is it true that the concatenation $L\varnothing$, where $L$ is any regular language, result in $\varnothing$?

Namely, does $L\varnothing$ = $\varnothing$?

Thanks a lot!

Answer 1

Yes. If $L$ and $M$ are 2 languages, then their concatenation is defined by $$LM = \{xy : x \in L, y \in M\}.$$ If $M = \varnothing$, then there is no $y \in M$, so the set on the right hand side is empty.