Answer whether the following statements are true or false. You don't need to show proof or

justify.

$(1)$ Let $G$ be a context$-$free grammar which is ambiguous. There may or may not exist

another context$-$free grammar $G^{\text{'}}$ satisfying the following two conditions:

$($i$)G$ and $G^{\text{'}}$ generate the same language.

$($ii$)G^{\text{'}}$ is not ambiguous.

$(2)$ The Turing$-$recognizable languages are closed under complementation.