Consider the set S = (A, B, C, D}. Consider the following 4 partitions π1, π2, π3, π4 on S : π1 = {ABCD}’ , π2 = {AB}’ , {CD}’ , π3 = {ABC}’ , {D}’ , π4 = A’ , B’ , C’ , D’. Let P be the partial order on the set of partitions S’ = {π1, π2, π3, π4} defined as follows : πi P πj if and only if πi refines πj. The poset diagram for (S’, P ) is :
(A)
(B)
(C)
(D)
Answer: (C)
Explanation:
A partition is said to refine another partition if it splits the sets in the second partition to a larger number of sets.
Corresponding Hasse diagram is Option C.
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