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Determine whether the relation R in the set A = {1, 2, 3, …., 13, 14} defined as R = {(x, y); 3x – y = 0} is reflexive, symmetric and transitive. |
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Answer» Given A = {1,2,3, ….,13, 14} R = {(x, y) : 3x - y =0} ∴ R= {1,3), (2, 6), (3, 9), (4, 12)} Here (1, 1) ∉ R, (2, 2) ∉ R R is not reflexive Here (1, 3) ∈ R but (3, 1) ∉ R ∴ R is not symmetric Here (1,3) and (3, 9)6 ∈ R but (1,9) ∉ R ∴ R is not transitive ∴ R is not an equivalence relation. |
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