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Let $X = \{1, 2, 3, .....\}$ be ordered by divisibility, which of the following subset is totally ordered ?

  1. $\{2, 9, 16\}$
  2. $\{3, 5, 15\}$
  3. $\{2, 6, 24\}$
  4. $\{4, 15, 30\}$
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A) $\{ 2 , 9 , 16 \}$

      2 is divisible by 1, 9 is not divisible by 2, 16 is not divisible by 3

B)$ \{ 3 , 5 , 15 \}$

     3 is divisible by 1, 5 is not divisible by 2, 15 is  divisible by 3

C) $\{ 2 , 6 , 24 \}$

      2 is divisible by 1 , 6 is divisible by 2, 24 is divisible by 3

D) $\{ 4 , 15 , 30 \}$

      4 is divisible by 1, 15 is not divisible by 2, 30 is divisible by 3

So, $\{2 , 6, 24 \}$ is totally ordered subset of $\{1 , 2, 3\}$

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