Question

is {(x1,x2)^T | x1^2=X2^2} a subset of R^2

Answer 1

\[\left\{\left(\begin{matrix}x_1\\x_2\end{matrix}\right):x_1^2=x_2^2\right\}\subseteq\mathbb{R}^2\]
is true so long as x_1 and x_2 are both real numbers (elements of R).