$$X\subset \mathbb R^n$$ a subspace with Euclidean metric on $\mathbb R^n.$ Then the $X$ that is complete is :
$A.X=\mathbb Z \times \mathbb Z\subset \mathbb R\times \mathbb R.$
$B.X=\mathbb Q\times \mathbb R\subset \mathbb R\times \mathbb R.$
$C.X=(-\pi,\pi)\cap\mathbb Q\subset \mathbb R.$
$D.X=[-\pi,\pi]\cap \mathbb Q^c\subset \mathbb R.$
For $A$ , I guess the only Cauchy sequences will be the constant sequences so that will be complete.
For $B$ , since $\mathbb Q$ is not complete in $\mathbb R$ , a Cauchy sequence can be found that will not converge in the given $X.$ So not complete.
For $C$ , a Cauchy sequence in the $X$ can be found that converges to $\pi$ or $-\pi$,thus not converging inside $X.$ So , not complete.
For $D$ , if $x\in [\pi,-\pi]\cap \mathbb Q$ , then I think we could find a Cauchy sequence in $X$ that converges to $x$ and thus $X$ in $D$ is also not complete.
Did I make any mistakes here $?$