1 votes 1 votes Ans. C Mathematical Logic lattice discrete-mathematics + – Na462 asked Aug 19, 2018 Na462 1.4k views answer comment Share Follow See all 23 Comments See all 23 23 Comments reply Na462 commented Aug 19, 2018 reply Follow Share Please Explain. 0 votes 0 votes arvin commented Aug 19, 2018 reply Follow Share A) false as its poset but lattice too(every pair of element will have a max and min) b)false its distributive lattice as distributive lattice has atmost 1 complement. c)true as its distributive and n>0 (givenn positive integer ) and its countably infinite so not bounded. d) false : its a poset as it satisfies reflexive,antisymm,transitive property. 0 votes 0 votes Rishav Kumar Singh commented Aug 19, 2018 reply Follow Share @arvin No element has even one complement right? It's hasse diagram will be chain right then it will be TOS? Can you explain how it is reflexive? 3 votes 3 votes arvin commented Aug 19, 2018 reply Follow Share yes (distributive lattice says every element should have atmost 1 complement) yes ( it will always be a chain) its reflexive because every element will be the divisor of itself... for eg : (1|1) (2|2) (4|4) .........................-->aRa =1 always 2 votes 2 votes Rishav Kumar Singh commented Aug 19, 2018 reply Follow Share Thanks, in this example is there any element with one complement.? I thinks there is not 1 votes 1 votes arvin commented Aug 19, 2018 reply Follow Share @rishav no bro no element has any complement. 1 votes 1 votes srestha commented Aug 21, 2018 reply Follow Share how it will be distributive? 0 votes 0 votes arvin commented Aug 21, 2018 reply Follow Share because it has no complement or 0 complement... and distributive lattice has atmost 1complement. 0 votes 0 votes Rishav Kumar Singh commented Aug 21, 2018 reply Follow Share Addition to Arvin, it is TOS in hasse diagram it will be a chain so, no presence of L1* and L2* 0 votes 0 votes srestha commented Aug 21, 2018 reply Follow Share is it a poset too? 0 votes 0 votes Rishav Kumar Singh commented Aug 21, 2018 reply Follow Share Yes mam 0 votes 0 votes srestha commented Aug 21, 2018 reply Follow Share how?? 0 votes 0 votes Rishav Kumar Singh commented Aug 21, 2018 reply Follow Share Because it is partial ordering relation, because it is Reflexive, antisymmetric and transitive. 0 votes 0 votes srestha commented Aug 21, 2018 reply Follow Share say for (2,4) how it will be antisymmetric? 0 votes 0 votes Rishav Kumar Singh commented Aug 21, 2018 reply Follow Share Because we can't find any pair (4,2) 1 votes 1 votes arvin commented Aug 21, 2018 reply Follow Share 2R4=2 which is one among the domain. But 4R2=.5 which is not in the domain. So it's antisymmetric. 1 votes 1 votes srestha commented Aug 21, 2018 reply Follow Share 4R2 not 4?? 0 votes 0 votes arvin commented Aug 21, 2018 reply Follow Share no mam here in the question they have mentioned that n is a +ve integer. and a is divisor of b. but 4 is not divisor of 2. 1 votes 1 votes srestha commented Aug 21, 2018 reply Follow Share yes, it is a chain every 2 element has a LUB and a GLB, that is why it is lattice but it no lower bound bound and no upper bound So, it is not bounded that means the lattice has LUB but no upper bound And can u tell me is it complemented lattice or not? I think it is complemented lattice too 0 votes 0 votes arvin commented Aug 21, 2018 i edited by arvin Aug 21, 2018 reply Follow Share its not a complemented lattice as to be complemented it has to satisfy two properties: 1)it should be bounded 2)it should have atleast one complement for each element. but it fails on both the criteria so its not a complemented lattice. 2 votes 2 votes Rishav Kumar Singh commented Aug 21, 2018 reply Follow Share Statement should be "it should have atleast one complement for every element" 0 votes 0 votes arvin commented Aug 21, 2018 reply Follow Share yes :p updated 0 votes 0 votes smsubham commented Dec 28, 2019 reply Follow Share @arvin distributive lattice says every element should have atmost 1 complement. No. Only its converse is true. See this: https://gateoverflow.in/265533/lattice 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes It is TOSET as it will form a chain. (2->4->8->16->32→…………..) As it is TOSET it will be Lattice. TOSET is bounded from below i.e least element is 2 but not bounded from above as it infinite. Hence not bounded lattice. As this TOSET forms a chain it will not have sublatice equivalent to KITE lattice or Pentagon Lattice. Correct option C. aaaakash001 answered Nov 7, 2022 aaaakash001 comment Share Follow See all 0 reply Please log in or register to add a comment.