Let S= {a,b,c,d,e} and P be the set of partitions of S such that P={P1,P2,P3,P4}, where P1={{a,b,c},{d,e}},P2={{a,b},{c,d,e}},P3={{a,b,c,d,e}} and P4= {{a},{b},{c},{d},{e}} A partial order is defined on P such that Pi ≤ Pj, if and only if all the elements of Pi are subsets of elements of Pj. (a) Express the partial order using a Hasse diagram. (b) Check whether it is a lattice. Explain your answer