GATE Computer Science (CS) 2020 Solved Papers

Let ${\mathit{L}}_1={\mathit{a}}^{\mathit{n}}{\mathit{b}}^{\mathit{n}}\Rightarrow \mathit{C}\mathit{F}\mathit{L}$
${\mathit{L}}_2={\mathit{\Sigma }}^{*}\Rightarrow$ Regular
${\mathit{L}}_1\cup {\mathit{L}}_2=\left({\mathit{a}}^{\mathit{n}}{\mathit{b}}^{\mathit{n}}\right)\cup {\mathit{\Sigma }}^{*}={\mathit{\Sigma }}^{*}\Rightarrow$ Regular
Since ${\mathit{L}}_1\cup {\mathit{L}}_2$ is regular but ${\mathit{L}}_1$ is not regular, Hence statement $\mathit{I}$ is false.
Regular language is not closed under infinite union.
Hence, statement-II is also false.
$\therefore$ Neither I nor II is true.