Which of the following statement(s) are true? (A) If $F _ { 1 } , F _ { 2 }$ are finite field extensions of $\mathbb { Q }$ such that $\left[ F _ { 1 } : \mathbb { Q } \right] = \left[ F _ { 2 } : \mathbb { Q } \right]$, then $F _ { 1 } , F _ { 2 }$ are isomorphic as fields. (B) If $F _ { 1 } , F _ { 2 }$ are finite field extensions of $\mathbb { R }$ such that $\left[ F _ { 1 } : \mathbb { R } \right] = \left[ F _ { 2 } : \mathbb { R } \right]$, then $F _ { 1 } , F _ { 2 }$ are isomorphic as fields. (C) Let $\mathbb { F }$ be a finite field. If $F _ { 1 } , F _ { 2 }$ be finite field extensions of $\mathbb { F }$ such that $\left[ F _ { 1 } : \mathbb { F } \right] = \left[ F _ { 2 } : \mathbb { F } \right]$, then $F _ { 1 } , F _ { 2 }$ are isomorphic as fields. (D) Let $\omega \in \mathbb { C }$ be a primitive cube root of unity and let $\sqrt [ 3 ] { 2 } \in \mathbb { R }$ be a cube root of 2. Let $K = \mathbb { Q } ( \omega , \sqrt [ 3 ] { 2 } )$. If $F _ { 1 } , F _ { 2 }$ are subfields of $K$ such that $\left[ K : F _ { 1 } \right] = \left[ K : F _ { 2 } \right] = 2$, then $F _ { 1 } = F _ { 2 }$.
Which of the following statement(s) are true?\\
(A) If $F _ { 1 } , F _ { 2 }$ are finite field extensions of $\mathbb { Q }$ such that $\left[ F _ { 1 } : \mathbb { Q } \right] = \left[ F _ { 2 } : \mathbb { Q } \right]$, then $F _ { 1 } , F _ { 2 }$ are isomorphic as fields.\\
(B) If $F _ { 1 } , F _ { 2 }$ are finite field extensions of $\mathbb { R }$ such that $\left[ F _ { 1 } : \mathbb { R } \right] = \left[ F _ { 2 } : \mathbb { R } \right]$, then $F _ { 1 } , F _ { 2 }$ are isomorphic as fields.\\
(C) Let $\mathbb { F }$ be a finite field. If $F _ { 1 } , F _ { 2 }$ be finite field extensions of $\mathbb { F }$ such that $\left[ F _ { 1 } : \mathbb { F } \right] = \left[ F _ { 2 } : \mathbb { F } \right]$, then $F _ { 1 } , F _ { 2 }$ are isomorphic as fields.\\
(D) Let $\omega \in \mathbb { C }$ be a primitive cube root of unity and let $\sqrt [ 3 ] { 2 } \in \mathbb { R }$ be a cube root of 2. Let $K = \mathbb { Q } ( \omega , \sqrt [ 3 ] { 2 } )$. If $F _ { 1 } , F _ { 2 }$ are subfields of $K$ such that $\left[ K : F _ { 1 } \right] = \left[ K : F _ { 2 } \right] = 2$, then $F _ { 1 } = F _ { 2 }$.