DM - Functions & Relations -Q16

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The number of relations, on a set of five elements, which are both equivalence relation and partial order relation is ______?
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

For a relation to be both Equivalence relation and Partial order relation, It has to be refelxive. Now consider the

identity relation i.e. I_A = \{ (a,a) | a \in A \}

To this relation if we add any one more ordered pair (a,b) where a \neq b , then either symmetric or antisymmetric property will violate. Hence,  the only relation that is both Equivalence relation and Partial order relation is  I_A = \{ (a,a) | a \in A \}

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