Traitor tracing - determining a set of codewords
Note that there are two words in $F$ which disagree on the $k^{th}$ coordinate if and only if  $|X(k)|&gt;1.$

All three words in $F$ have $0$ as their first symbol so $X(1)=\{0\}.$

Thus all descendants have 0 in their first coordinate.

By definition of the direct product $\times,$ the descendants are formed by entering all elements of $X(1)$ in the first coordinate, those of $X(2)$ in the second coordinate, etc.