GATE CSE 1996 | Question: 1.2

Question

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

• A. $3$
• B. $4$
• C. $9$
• D. None of the above

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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abir_banerjee

what do you mean by “implicit edges”?

Answer 1

Answer: B

Hasse Diagram is$:$

Comments

We don't represent transitive edges in Hasse diagram.

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Also, the reflexive loops are not represented.

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@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. 

Answer 2

                                        24

                                         /

                                       12

                                       /

                                    6

                               /      \

                             2        3

Now u can count number of edges will be 4.

Answer 3

Elements can be related like below as well. 

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.

Answer 4

.