I am taking a course on Automaton where I faced the algebraic laws of regular expressions.
First two were ok:
$\emptyset + L = L + \emptyset = L$: Union of a language $L$ with empty language gives the language $L$ itself.
$\epsilon L = L\epsilon = L$: Concatenation of empty string with strings belonging to certain language $L$ gives back the set of string of language $L$
But the third one is confusing me:
- $\emptyset L = L\emptyset = \emptyset$
I felt it should be $\emptyset L = L\emptyset = L$, since concatenation of strings of language L with string of empty language which is essentially no strings at all (which essentially means nothing to concatenate), should give back the language $L$ itself. Where I am thinking wrong?