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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 π1, π2, π3, π4 on S : π1 = {\overline{ABCD} }, π2 = {\overline{AB}, \overline{CD}}, π3 = {\overline{ABC},\overline{D}}, π4 = {\overline{A},\overline{B},\overline{C},\overline{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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Last Updated : 13 Nov, 2017
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