Determine whether each of the following relations are reflexive, symmetric and transitive. (i) Relation R in...

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Determine whether each of the following relations are reflexive, symmetric and transitive. (i) Relation R in the set A={1,2,3,...,13,14} defined as R = {(x, y): 3x - y = 0} (ii) Relation R in the set of N natural numbers defined as R = {(x, y): y = x + 5 and .x < 4} (iii) Relation R in the set A={1,2,3,4,5,6} defined as R={(x, y): y is divisible by x} (iv) Relation R in the set of Z integers defined as R = {(x, y): x-y is an integer} (v) Relation R in the set of human beings in a town at a particular time given by R = {(x, y): x and y work at the same place} (a) (b) (c) (d) (e) R = {(x, y): x and y live in the same locality} R={(x,y): x is exactly 7cm taller than y} R={(x, y): x is wife of y} R={(x, y): x is father of y} Determine whether each of the following relations are reflexive, symmetric and transitive. (i) Relation R in the set A={1,2,3,...,13,14} defined as R = {(x, y): 3x - y = 0} (ii) Relation R in the set of N natural numbers defined as R = {(x, y): y = x + 5 and .x < 4} (iii) Relation R in the set A={1,2,3,4,5,6} defined as R={(x, y): y is divisible by x} (iv) Relation R in the set of Z integers defined as R = {(x, y): x-y is an integer} (v) Relation R in the set of human beings in a town at a particular time given by R = {(x, y): x and y work at the same place} (a) (b) (c) (d) (e) R = {(x, y): x and y live in the same locality} R={(x,y): x is exactly 7cm taller than y} R={(x, y): x is wife of y} R={(x, y): x is father of y}

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