6.2.2 Binary relations

Problem: Find the domain of definition, the domain of values of the relation \( P \). Is the relation \( P \) reflexive, antireflexive, symmetrical, antisymmetric, nonsymmetrical, transitive? What class of relations does it belong to? Justify your answer. \[ P \subseteq R^{2},(x, y) \in P \Leftrightarrow x \cdot y>1 . \]