6.2.27 Binary relations

Condition: The binary relation \( R \) on the set \( \{1,2,3,4\} \) is given. Check it for reflexivity, symmetry, antisymmetry, transitivity. Find \( \delta_{R}, \rho_{R}, R^{-1}, R^{2} \); depict the indicated binary relations on the coordinate plane. \[ \{\langle 1,1\rangle,\langle 1,4\rangle,\langle 2,2\rangle,\langle 2,3\rangle,\langle 2,4\rangle,\langle 3,3\rangle,\langle 3,4\rangle,\langle 4.4\rangle\} \]