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Let $\text{N}^{+}$ denote the non-zero positive integers. Define a binary relation $\text{R}$ on $\text{N}^{+} \times \text{N}^{+}$ by $(m, n)\text{R}(s, t)$ if $\gcd(m, n) = \gcd(s, t).$ The binary relation $\text{R}$ is

  1. Reflexive
  2. Symmetric
  3. Transitive
  4. Not Transitive
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Reflexive because $(a,b) \text{R} (a,b)$

Symmetric because $\gcd(m,n) = \gcd(s,t)$ implies that $\gcd(s,t) = \gcd(m,n)$

Transitive because $\gcd(m,n) = \gcd(s,t)$ and $\gcd(s,t) = \gcd(a,b)$ implies that $\gcd(m,n) = \gcd(a,b)$
Answer:

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