Question 12
Call a set $S$ *product-free* if there do not exist $a,$ $b,$ $c \in S$ (not necessarily distinct) such that $ab = c.$ For example, the empty set and the set $\{16, 20\}$ are product-free, whereas the sets $\{4, 16\}$ and $\{2, 8, 16\}$ are not product-free. Find the number of product-free subsets of the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}.$