Take $A = \{0,1\}$. Now if we find all the subsets of binary relation i.e. $A\times A$ we get one of them as $R = \emptyset$. Now I can understand that $R$ does not have $(0,0)$ and $(1,1)$. So $R = \emptyset$ is not reflexive. But how is it symmetric and transitive?
[Math] Why is $\emptyset$ symmetric and transitive
discrete mathematicsrelations
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Best Answer
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.