in Set Theory & Algebra
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Consider the following Posets:

$I)\left ( \left \{ 1,2,5,7,10,14,35,70 \right \},\leq \right )$

$II)\left ( \left \{ 1,2,3,6,14,21,42 \right \},/ \right )$

$III)\left ( \left \{ 1,2,3,6,11,22,33,66 \right \},/ \right )$

Which of the above poset are isomorphic to $\left ( P\left ( S \right ),\subseteq \right )$ where $S=\left \{ a,b,c \right \}?$
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Option 3...?
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yes, elaborate
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2 Answers

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Best answer

This can be solved easily by drawing a Hasse Diagram..

See that all the properties of isomorphic graphs (same number of edges and vertices, connectivity preservation) are satisfied.

So option 3 is Ans

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I) and II) also can done in similar way

right??
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Yaa...(I) will result in a chain..So isomorphism not satisfied..and for 2 also isomorphism will not be satisfied but hasse diagram can surely be drawn..
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This poset has 8 nodes in hasse diagram.

So its isomorphic poset should also have 8 nodes.

So option 2 eliminated as it has only 7 nodes.

Option 1 is a chain so we cant get the cube like structure.

So optiion 1 also eliminated.

$\therefore$ Option 3 is the correct answer.

If we draw it we will get same stucture of hasse diagram as shown above.

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