A set of positive integers $X$ is called connected if $|X|\ge 2$ and there exist two distinct elements $m$ and $n$ of $X$ such that $m$ is a divisor of $n$. Determine the number of connected subsets of the set $\{1,2,\ldots,10\}$.
Source: Pan African Olympiad 2008
Tags: combinatorics proposed, combinatorics
A set of positive integers $X$ is called connected if $|X|\ge 2$ and there exist two distinct elements $m$ and $n$ of $X$ such that $m$ is a divisor of $n$. Determine the number of connected subsets of the set $\{1,2,\ldots,10\}$.