MathNet 2010 — Part 07 Question 132

Let $S=\{1,2,3,4,5,6,7,8,9,10\}$. How many (potentially empty) subsets $T$ of $S$ are there such that, for all $x$, if $x$ is in $T$ and $2x$ is in $S$ then $2x$ is also in $T$?