6.2.25 BINARY RELATIONS

Condition: for set on the set \ (a = \ {1,2,3,4,5 \} \) binary relationships \ (\ rho \) and \ (\ tau \): a) write matrices and build graphics: b) matrix method to find the composition \ (\ rho \ circ \ tau \), build a ratio of relations; d) investigate the properties of relations \ (\ rho, \ tau \) and \ (\ rho \ circ \ tau \) (reflexivity, irreflexivity, symmetry, anti -symmetry, transitivity). \ [\ begin {array} {l} \ rho = \ {(x, y): x+y = 0 (\ bmod 2) \} \\ \ tau = \ {(x, y): 2 \ leq y \ leq x-1 \ ent {array} \] \] \] \] \] \] \] \] \] \] \] \] \] \] \]