Question

Is ϕ REFLEXIVE on R(ϕ->ϕ)?

Answer 1

It's symmetric and transitive by a phenomenon called vacuous truth. Symmetricity and transitivity are both formulated as "Whenever you have this, you can say that". In the case of the trivially false relation, you never have "this", so the properties stand true, since there are no counterexamples.

Answer 2

Phi is not Reflexive bt it is Symmetric, Transitive.

Comments

Relation PHI
ON
PHI to PHI set.

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(Phi, Phi) != Phi

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∅ x ∅ = ∅  ​

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Phi is irreflexive, symmetric and transitive.

Answer 3

I think it is.

Answer 4

TRUE

This is a reflexive relation.

Since there is no element in the domain

so we can say that

for all x, xRx is True. 

but phi is not a reflexive relation when the domain is not empty.

and By default, when it is not mentioned we should take that the domain is not empty.