Notation for total number of sets?

Question

I have sets $B$ and $X_1, ..., X_n$. There could be any number of $X$ sets, but at least one, and always set $B$.

$(B + (X_1, ..., X_n)) = n$ or total number of sets.

How do I write the total number of sets correctly?

Answer 1

You have a set of sets , namely A= {$\text { B, $X_1$, $X_2$,..., $X_n$}$}

Thus you write $|A|= n+1$

Answer 2

Define the family of sets indexed by $n$ to be $\{X_i\}_{i=1}^n$.

Taking $\{X_i\}^{n}_{i=1} \cup \{B\} = \{X_i\}^{n}_{i=1}$

Therefore, the family adjoined with $B$ can still be indexed by $n$.