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GATE | GATE-CS-2007 | Question 26

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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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