GATE | GATE-CS-2007 | Question 26
Consider the set S = (A, B, C, D}. Consider the following 4 partitions Ï€1, Ï€2, Ï€3, Ï€4 on S : Ï€1 = {ABCD}’ , Ï€2 = {AB}’ , {CD}’ , Ï€3 = {ABC}’ , {D}’ , Ï€4 = A’ , B’ , C’ , D’. 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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