Question: For each relation below, explain why the relation does or does not satisfy each of the properties reflexive, symmetric, antisymmetric, and transitive. (a) isBrotherOf on

For each relation below, explain why the relation does or does not satisfy each of the properties reflexive, symmetric, antisymmetric, and transitive.

(a) isBrotherOf on the set of people.

(b) isFatherOf on the set of people.

(c) The relation R = {hx, yi | x 2 + y 2 = 1} for real numbers x and y.

(d) The relation R = {hx, yi | x 2 = y 2} for real numbers x and y.

(e) The relation R = {hx, yi | x mod y = 0} for x, y {1, 2, 3, 4}.

(f) The empty relation (i.e., the relation with no ordered pairs for which it is true) on the set of integers.

(g) The empty relation (i.e., the relation with no ordered pairs for which it is true) on the empty set.

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