Let I be the poset (partially ordered set) with Hasse diagram 0-1 and In = I x I x .. I = { (e1,e2,...,en | ei is element of {0,1} } be the direct product of I with itself n times ordered by : (e1,e2,..,en) <= (f1,f2,..,fn) in In if and only if ei <= fi for all i= 1,..,n.
a)Show that (In,<=) is isomorphic to ( 2[n],⊆)
b)Show that for any two subset S,T of [n] = {1,2,..n}
M(S,T) = (-1)IT-SI if S ⊆ T , 0 otherwise.
PLEASE SOLVE A AND B NOT SINGLE PART !!!