We can use closure properties to help prove certain languages are not regular. Start with the fact that the language $L_{0n1n}=\{0^{n}1^{n}|n\geq 0\}$ is not a regular set. Prove the following languages not to be regular by transforming them using operations known to preserve regularity,to $L_{0n1n}:$
- $\{0^{i}1^{j}|i\neq j\}$
- $\{0^{n}1^{m}2^{n-m}|n\geq m\geq 0\}$
