Relation

Question

State True or False?

Empty set Φ is an equivalence relation.

Comments

on which set you are applying this relation?

if the set is non-empty, then it is trivial to say false

but what is the answer, if the set is EMPTY?

check this https://gateoverflow.in/229165/self-doubt

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given that it will be irreflexive

but here https://math.stackexchange.com/questions/1203676/is-an-empty-set-reflexive-symmetric-transitive

it is given that empty set contain equivalence relation

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ANY SET OF ELEMENTS??? GIVEN OVER THAT RELATION IS TO BE FORMED

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Yes right as Shaik Masthan said that if the relation is formed from a non-empty set, then empty set is not an equivalence relation as the smallest equivalence relation must contain the diagonal elements i.e. (a,a);(b,b) and so on 

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@Sayan Bose

SO IF SET IS EMPTY THEN

I AM NOT ABLE TO DRAW CONCLUSION FROM https://gateoverflow.in/229165/self-doubt

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Yes I have seen the discussion on that link. Which part are you not able to understand ?

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THAT PICTURE IS NOT LOADING AT THAT TIME. FROM PICTURE I UNDERSTAND :)

Answer 1

There is one thing relationship

Empty relation on empty set is reflexive,irreflexive, symmetry, assymetric, antisymmetric and transtive

Empty relation on non empty set  is irreflexive, symmetry, asymmetric, antisymmetric, transtive.

Comments

short and simple :)

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Can a relation be both reflexive and irreflexive.If yes can you please give examples.Aren't reflexive and irreflexive both mutually exclusive sets?

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@sripo

Empty relation on empty set or both reflexive and irreflexive, it's only example I know , and you will find many material where proof is given