Hey guys. I have this problem:

Let $\displaystyle A = \left\{1,2,...,12\right\}$. Give an example of a partition S of A satisfying the following requirements:

(i) |S| = 5,

(ii) there is a subset T of S such that |T| = 4 and $\displaystyle |\cup_{X\in T} X|$ = 10 and

(iii) there is no element$\displaystyle B \in S$ such that |B| = 3.

I need help understanding what the second part of (ii) means. I was able to create a partition that I think satisfies the other conditions. I just don't see how $\displaystyle |\cup_{X\in T} X|$ could have a cardinality of 10 when the subset T has only 4 elements.

$\displaystyle S=\left\{\left\{1,2,3,4\right\},\left\{5,6\right\} ,\left\{7,8\right\},\left\{9,10\right\},\left\{11, 12\right\} \right\}$

subset $\displaystyle T=\left\{1,2,3,4\right\}$