22 votes 22 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 $3$ $4$ $9$ None of the above Set Theory & Algebra gate1996 set-theory&algebra partial-order normal + – Kathleen asked Oct 9, 2014 • edited Jun 7, 2018 by Milicevic3306 Kathleen 13.4k views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply Thadymademe commented Aug 12, 2022 reply Follow Share @Deepak Poonia Sir if the question had asked about number of edges including the implicit edges then the answer would have been same?? 0 votes 0 votes Pranavpurkar commented Oct 22, 2022 reply Follow Share abir_banerjee what do you mean by “implicit edges”? 0 votes 0 votes Please log in or register to add a comment.
Best answer 32 votes 32 votes Answer: B Hasse Diagram is$:$ Rajarshi Sarkar answered May 11, 2015 • edited May 10, 2019 by Lakshman Bhaiya Rajarshi Sarkar comment Share Follow See all 4 Comments See all 4 4 Comments reply Sachin Mittal 1 commented Jan 8, 2017 reply Follow Share We don't represent transitive edges in Hasse diagram. 8 votes 8 votes Ayush Upadhyaya commented Jan 1, 2018 reply Follow Share Also, the reflexive loops are not represented. 6 votes 6 votes ankit3009 commented Oct 4, 2021 reply Follow Share @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. 0 votes 0 votes rhl commented May 11, 2022 reply Follow Share @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. 0 votes 0 votes Please log in or register to add a comment.
6 votes 6 votes 24 / 12 / 6 / \ 2 3 Now u can count number of edges will be 4. Paras Nath answered Sep 21, 2016 Paras Nath comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Elements can be related like below as well. roh answered May 10, 2020 roh comment Share Follow See all 2 Comments See all 2 2 Comments reply Hradesh patel commented May 11, 2020 reply Follow Share No ...I think this is wrong because what about in between 12 and 24 relation. 2 votes 2 votes DAWID15 commented Dec 12, 2021 reply Follow Share 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. 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes . akshay_123 answered Sep 24, 2023 akshay_123 comment Share Follow See all 0 reply Please log in or register to add a comment.