Possible cardinalities of the union of two sets

Question

So the question is:

What are the possible cardinalities of the union of the two sets $A$ (where $[A] = 5$) and $B$ (where $[B] = 9$)

So, the smallest $[A \cup B]$ is when all elements of $A$ are also elements of $B$. Then, $[A \cup B]$ in this case is:

(those 5 similar elements) + (the remaining 4 in B) = 9

And the largest $[A \cup B]$ is when no element of A is in B Then, $[A \cup B]$ in this case is:

$[A] + [B] = 14$

Then the possible cardinalities of $[A \cup B]$ is:

9, 10, ... , 14

I don't understand how my reasoning is incorrect. My book says that 6 is a possible cardinality. The only explanation I could think of is that one or both of the sets has duplicate elements. But, wouldn't the cardinality of a set with duplicate elements be the amount of unique elements?

Edit: I actually worded the question for the sake of my explanation. The actual question is:

We form the union of a set with 5 elements and a set with 9 elements. Which of the following numbers can we get as the cardinality of the union: 4, 6, 9, 10, 14, 20

Answer 1

Your reasoning is correct. More simply, $6$ can't possibly be the cardinality of the union, since the union must contain at least as many elements as $B$! It seems that the book just has an error in the solution.