DM - Functions & Relations -Q8

+1 vote
The total number of different equivalence relations possible on a set of 5 elements?
asked Jun 24 in Discrete Maths by gbeditor (44,500 points)
reshown 6 days ago by gbeditor

1 Answer

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Best answer

Number of equivalence relations = Number of possible partitions

Partition into one set : 1 Way

Partition into two sets : (4,1) = 5 Ways ; (3,2) = 5C2 Ways

Partition into three sets : (3,1,1) = 5C3 Ways ; (2,2,1) = 5C1 * (4C2  /  2!)  Ways

Partition into four sets : (2,1,1,1) = 5C2 Ways

Partition into five sets : 1 Way

Total = 52


Method 2 :

The number of equivalence relations on a set of 5 elements = bell number

image

so 52

https://en.wikipedia.org/wiki/Bell_number

answered 4 days ago by deepak-gatebook (112,390 points)
Answer:
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