6.2.20 Binary relations

Condition: For binary relations \( \rho \) and \( \tau \) given on the set \( A=\{1,2,3,4,5\} \): a) write down matrices and construct graphs; b) find the composition \( \rho \circ \tau \); c) explore the properties of the relations \( \rho, \tau \) and \( \rho \circ \tau \) (reflexivity, irreflexivity, symmetry, antisymmetry, transitivity). \[ \begin{array}{l} \rho=\{(x, y)|2 \leq| x-2 y \mid \leq 4\} \\ \tau=\{(x, y) \mid x+y+1 \equiv 1(\bmod 2)\} \end{array} \]