How to write single definition for two indexed matrices in a single line?

Question

I want to define $X_i$ and $X_j$ as

$X_{i} = \left\{x_k| {x}_k \in \mathcal{C}_{i} \right\}$

and

$X_{j} = \left\{x_k| {x}_k \in \mathcal{C}_{j} \right\}$

How can I combine these definition together in a correct notation?

Something like the following line, though I am not sure if it is mathematically same as above definitions: $X'_{\{i,j\}} = \left\{{x}_k| {x}_k \in \mathcal{C}_{\{i,j\}} \right\}$

Answer 1

You can write something like $$ X_a = \{x_k \mid x_k \in \mathcal C_a\}, \quad a \in \{i,j\} $$ Writing the set $\{i,j\}$ as index as you did in your proposal seems unusual to me.