If N² = N × N, where N is the set of natural numbers, and R is a relation on N² such that ⟨x, y⟩ R ⟨u, v⟩ ⇔ xv = yu, which of the following are TRUE?
(A) Reflexive
(B) Symmetric
(C) Transitive
(D) Asymmetric
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Correct answer: D. (A), (B) and (C) Only
Explanation
xv = yu means x/y = u/v (equality of fractions). xy = yx (reflexive), the condition is symmetric, and equal ratios chain (transitive). It is an equivalence relation, not asymmetric.More Discrete Structures and Optimization questions
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