6.2.26 Binary relations

condition: For binary relations \( \rho \) and \( \tau \) given on the set \( A=\{1,2,3,4,5\} \): a) write matrices and construct graphs: b) use the matrix method to find the composition \( \rho \circ \tau \), construct a graph of the relation: c) explore the properties of the relations \( \rho, \tau \) and \( \rho \circ \tau \) (reflexivity, irreflexivity, symmetry, antisymmetry, transitivity). \[ \rho=\{(x, y):|x-y| \geq 2\}, \quad \tau=\{(x, y): x(6-y) \leq 8, x \neq y\} . \]