(4) For each of the following relations, determine all of the properties which it satisfies in...

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(4) For each of the following relations, determine all of the properties which it satisfies in the following list: reflexive, symmetric, transitive, antisymmetric, weakly antisym- metric. You should justify why it satisfies a property or not. = (a) X (b) X = {a, b, c} and R = = {a,b,c} and R = {(a, b), (b, a), (c, a), (a, c)}. {(a, a), (b,b), (c, c), (a, c), (c, a)}. {(x, y) = Z Z : |x y| < 3}. (c) X = Z and R = (d) X = Z and R = {(x, y) = Z Z : x - y < 3}. (e) X = = Z/8Z and R = {(x, y) = Z/8Z : xy = 0 mod 8}. (4) For each of the following relations, determine all of the properties which it satisfies in the following list: reflexive, symmetric, transitive, antisymmetric, weakly antisym- metric. You should justify why it satisfies a property or not. = (a) X (b) X = {a, b, c} and R = = {a,b,c} and R = {(a, b), (b, a), (c, a), (a, c)}. {(a, a), (b,b), (c, c), (a, c), (c, a)}. {(x, y) = Z Z : |x y| < 3}. (c) X = Z and R = (d) X = Z and R = {(x, y) = Z Z : x - y < 3}. (e) X = = Z/8Z and R = {(x, y) = Z/8Z : xy = 0 mod 8}.