To clear this up, lets look at an example.
Let set \(A\)=\(\left\{10,11,12\right\}\) and set \(B=\left\{11,12,13,14\right\}\).
\(A\cup B=\left\{10,11,12,13,14\right\}\) (Notice each element is only listed once even though each set shares common elements)
\(A\cap B=\left\{11,12\right\}\) (Notice both sets share these elements)
\(\left|A\right|=3\) and \(\left|B\right|=4\)