Consider the set S = (A, B, C, D}. Consider the following 4 partitions π1, π2, π3, π4 on S : π1 = {
}, π2 = {
}, π3 = {
}, π4 = {
}. Let P be the partial order on the set of partitions S’ = {Ï€1, Ï€2, Ï€3, Ï€4} defined as follows : Ï€i P Ï€j if and only if Ï€i refines Ï€j. 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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Last Updated :
13 Nov, 2017
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