Self Doubt

Question

The question is asking, which of the following is a Toset. How to conclude on seeing the hasse diagrams of D1 and D2.

Comments

B..?

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Yes B, only D2 is a Toset.

Please elaborate.

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I am suddenly not being able to upload any pictures here i don't know why :/

Total ordered set or Toset means there should be chain and every pair of elements should be comparable i.e. the elements form a straight line for which toset is also known as linear ordered. For more : https://www.quora.com/How-can-you-explain-partial-order-and-total-order-in-simple-terms

For D1, the divisors of 24 are {1,2,3,4,6,8,12,24} and if you draw the poset you will get a structure like : https://studylib.net/doc/7330070/lattices (D₂₄ Pg 6 right side)

For D2, the divisors of 81 are {1,3,9,27,81} and the poset looks like :

1----3----9----27----81

A straight chain hence toset

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It's ok I have constructed the diagrams, but was not able to conclude. Thank you for the explanation and links. :)