User:Metajellyfish/Math720/MT1 4

Let $B_n$ be the poset $\{1, \dots, n \}$, ordered by the relation $\subseteq$. Prove that the $\mu$ function for any two $x \subseteq y \in B_n$ is $\mu (x,y) = (-1)^{|y|-|x|}$, and $\mu (x,y) = 0$ for $x \supset y$.