Choose the correct statement(s) from below: (A) There exists a subfield $F$ of $\mathbb{C}$ such that $F \nsubseteq \mathbb{R}$ and $F \simeq \mathbb{Q}[X]/(2X^3 - 3X^2 + 6)$; (B) For every irreducible cubic polynomial $f(X) \in \mathbb{Q}[X]$, there exists a subfield $F$ of $\mathbb{C}$ such that $F \nsubseteq \mathbb{R}$ and $F \simeq \mathbb{Q}[X]/f(X)$; (C) There exists a subfield $F$ of $\mathbb{R}$ such that $F \simeq \mathbb{Q}[X]/(2X^3 - 3X^2 + 6)$; (D) For every irreducible cubic polynomial $f(X) \in \mathbb{Q}[X]$, there exists a subfield $F$ of $\mathbb{R}$ such that $F \simeq \mathbb{Q}[X]/f(X)$.
Choose the correct statement(s) from below:\\
(A) There exists a subfield $F$ of $\mathbb{C}$ such that $F \nsubseteq \mathbb{R}$ and $F \simeq \mathbb{Q}[X]/(2X^3 - 3X^2 + 6)$;\\
(B) For every irreducible cubic polynomial $f(X) \in \mathbb{Q}[X]$, there exists a subfield $F$ of $\mathbb{C}$ such that $F \nsubseteq \mathbb{R}$ and $F \simeq \mathbb{Q}[X]/f(X)$;\\
(C) There exists a subfield $F$ of $\mathbb{R}$ such that $F \simeq \mathbb{Q}[X]/(2X^3 - 3X^2 + 6)$;\\
(D) For every irreducible cubic polynomial $f(X) \in \mathbb{Q}[X]$, there exists a subfield $F$ of $\mathbb{R}$ such that $F \simeq \mathbb{Q}[X]/f(X)$.