Question $2$

$(5$ marks$)$

Prove by contradiction that the following language is not regular.

$L_2=\{0^n{1}^m$:$nm,n0,m0\}$

Do NOT use the Pumping Lemma.

Instead, make use of closure properties of operations on regular languages, and make use of the fact that the

language $A=\{0^n{1}^n$:$n0\}$ is not regular $($proven in Lecture $12).$