Let X≠ ∅. We define the binary relation R on the potential set P (X) by the formula (A, B) ∈ R ⇔ (A ∩ B) ≠ ∅ Find out whether and under what circumstances this relation is reflexive, symmetric,...

Let X≠ ∅. We define the binary relation R on the potential set P (X) by the formula (A, B) ∈ R ⇔ (A ∩ B) ≠ ∅ Find out whether and under what circumstances this relation is reflexive, symmetric, antisymmetric, transitive. The solution must include the whole process and all the intermediate steps leading to the solution. The answer itself,
even if it was right, it is not enough!