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Determine w hether 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 N of natural numbers defined as R = {(x,y): y = x +5 and x lt 4} (iii) Relation R in the setA ={1,2,3,4,5,6}as R = {(x,y):y is divisible by x} (iv) Relation R in the set Z of allintegers defined as R= {(x, y) : x -y is an integer} (v) Relation R in the set A of human beings in a town at a particular time given by (a)R = {(x,y) : x andy work at the same place} (b) R = {(x,y):x and y live in the same locality] (c ) R ={(x,y) :x is exactly 7 cm taller than y} (d)R = {(x,y) :x is wife of y} (e) R = {(x,y):xis father of y} |
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Answer» (ii) Neither reflexive nor symmetric but transitive. (iii) Reflexive and transitive but not symmetric. (iv) Reflexive, symmetric and transitive. (v) (a) Reflexive, symmetric and transitive. (B) Reflexive, symmetric and transitive. (C ) Neither reflexive nor symmetric nor transitive. (d) Neither reflexive nor symmetric but transitive. (E) Neither reflexive nor symmetric nor transitive. |
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