For each of the following relations r on the set x decide whether r is reflexive, symmetric, (weakly) antisymmetric or transitive: (a) x = z, arb if and only if a ≤ b + 1; (b) x = z, arb if and only if a + b is even; (c) x = p, arb if and only if a and b are coprime: (d) x = z, arb if and only if a + b is divisible by 3; (e) x = r, arb if and only if a2 ≤ b2; (f ) x = r × r, (a, b)r(c, d) if and only if a = c; (g) x = n × n, (a, b)r(c, d) if and only if either a < c or(a = c and b ≤ d).