in Set Theory & Algebra edited by
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19 votes
19 votes

Let $X = \{2, 3, 6, 12, 24\}$, Let $\leq$ be the partial order defined by $X \leq Y$ if $x$ divides $y$. Number of edges in the Hasse diagram of $(X, \leq)$ is

  1. $3$
  2. $4$
  3. $9$
  4. None of the above
in Set Theory & Algebra edited by
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2 Comments

@Deepak Poonia Sir if the question had asked about number of edges including the implicit edges then the answer would have been same??

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what do you mean by “implicit edges”?

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4 Answers

28 votes
28 votes
Best answer

Answer: B

Hasse Diagram is$:$

edited by

4 Comments

We don't represent transitive edges in Hasse diagram.

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8
Also, the reflexive loops are not represented.
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6
@Sachin Sir, your diagram and @Rajarshi’s Sir diagram seems similar, I know transitive relation should be removed for hasse diagram. But here what you mentioned, I didn’t understood. Please help.
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@ankit3009 I think previously the diagram was different from what it is now and notice Lakshman sir edited it after Sachin sir's comment. So most probably lakshman sir rectified the error. 

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6 votes
6 votes

                                        24

                                         /

                                       12

                                       /

                                    6

                               /      \

                             2        3

Now u can count number of edges will be 4.

0 votes
0 votes

Elements can be related like below as well. 

by

2 Comments

No ...I think this is wrong because what about in between 12 and 24 relation.
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if any relation can be inferred from transitive property then there is not need to give a edge. 

Here 6 divides 12 and 12 divides 24 so by transitivity 6 can also divide 24. So edge from 12 to 24 is required. edge from 6 to 24 is useless.

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–3 votes
–3 votes

The correct answer is,(B) 4

Answer:

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