Let N be the set of natural numbers and R the relation on N × N defined by (a, b) R (c, d) if ad(b + c) = bc(a + d). Then R is
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Correct answer: D. An equivalence relation
Explanation
Dividing by abcd: (b + c)/(bc) = (a + d)/(ad), i.e. 1/c + 1/b = 1/d + 1/a, i.e. 1/a − 1/b = 1/c − 1/d. Equality of the value 1/a − 1/b is reflexive, symmetric and transitive.More Discrete Structures and Optimization questions
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