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

  1. $(2,6,24)$
  2. $(3,5,15)$
  3. $(2,9,16)$
  4. $(4,15,30)$
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As you know that (D,/) is a POSET (partially ordered set) if it fulfills three properties of,

  • Reflexivity 
  • Antisymmetric 
  • Transitivity 

In addition to these, if all elements in your set  also are comparable with each other.all element in a set are comparable with respect to division operator then POSET is TOSET.

Option A ALL element are comparable  with  respect to division operator (  6 divided by 2,24 divided by 6 and 2).

option B Here 3,5 are not comparable (5 not divide by 3 or 3 not divide by 5)

option C Here (2,9 ),(16,9) are not comparable (9 not divide by 2 or 16 not divide by 9)

option D Here (4,15),(4,30) are not comparable (15 not divide by 4 or 30 not divide by 4)

OPTION A

 

Answer:

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