# Made Easy Test Series:Discrete Mathematics-Poset

190 views
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 $S=\left \{ a,b,c \right \}?$
0
Option 3...?
0
yes, elaborate

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

selected by
0
I) and II) also can done in similar way

right??
1
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..

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.

## Related questions

1
1.5k views
Consider the poset $( \{3,5,9,15,24,45 \}, \mid).$ Which of the following is correct for the given poset ? There exist a greatest element and a least element There exist a greatest element but not a least element There exist a least element but not a greatest element There does not exist a greatest element and a least element
1 vote
Consider the following first order logic statement $I)\forall x\forall yP\left ( x,y \right )$ $II)\forall x\exists yP\left ( x,y \right )$ $III)\exists x\exists yP\left ( x,y \right )$ $III)\exists x\forall yP\left ( x,y \right )$ ... $II)$ is true , then $III),IV)$ is true $B)$ If $IV)$ is true , then $II),III)$ is true $C)$ None of these