Cardinality of $S=\{A,B\}$ where $A=B=\{1,2,3\}$. 
Given a set $S = \{A,B\}$ such that $A = \{1,2,3\}$ and $B = \{1,2,3\}$, what is the cardinality of S? 

I know this may seem very trivial, and I am inclined to believe that the answer is $2$; my question comes from the fact that $A = B$. Since both $A$ and $B$ are the same, would that not be the same as having a repeated element, therefore making the answer $1$?  

$S$ has one element, so has cardinality $1$.  (Although we have two labels for $\{1,2,3\}$, there is still only one such set.)  Sets don't have duplicates.  (Multisets can have duplicates.  If $S$ were a multiset, it would have cardinality $2$.)  The set $\{x, x, x, x, x, x, x, x\}$ has one element, $x$.
