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NEST2025MathematicsBasics of Mathematics

Let R be the equivalence relation on N 1 = n N : n 2 defined by for m, n N 1 , m R n if m n is a rational number. Then

Options

  1. Am and n have the same number of distinct prime divisors whenever m R n
  2. Bthe number of equivalence classes is finite
  3. Call prime numbers are in the same equivalence class
  4. Dthere exists an equivalence class with finitely many elements

Correct answer

A. m and n have the same number of distinct prime divisors whenever m R n

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