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Recent questions tagged lattice

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The number of totally ordered set compatible to the given POSET are __________
asked May 20, 2019 in Set Theory & Algebra srestha 483 views
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I Have doubt about the language. Is it asking about the sum of elements if we make the GBL set for the given lattice .
asked May 20, 2019 in Set Theory & Algebra Shawn Frost 117 views
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Can a countable infinite lattice be bounded?
asked Apr 20, 2019 in Set Theory & Algebra Manoj Kumar Pandey 161 views
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Let $A=\left \{ 1,2,3 \right \}$. A relation $R$ on $A\times A$ is defined by $\left ( a,b \right )R\left ( c,d \right )\Leftrightarrow \left ( “a\leq c “and” b\leq d “\right )$ S1:$R$ partial order S2: The poset $\left [ A\times A:R \right ]$ is a lattice Among S1 and S2 which one is true?
asked Feb 27, 2019 in Set Theory & Algebra srestha 482 views
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According to the answer first is’nt well ordered but we do have least element 0 there, how is 0 not least element?
asked Jan 21, 2019 in Mathematical Logic bts1jimin 158 views
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asked Nov 15, 2018 in Mathematical Logic Na462 1.5k views
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Prove that every complete lattice is bounded lattice but not vice-versa .
asked Oct 23, 2018 in Graph Theory Gurdeep Saini 524 views
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What is dual of a lattice? Also give an example
asked Aug 31, 2018 in Set Theory & Algebra sakharam 308 views
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Consider F be a family of all subsets of set {1, 2, 3, ..... 100} that contain atleast 50 numbers, partially ordered with respect to containment. Then maximum size of chains in the Poset (F, ⊆) that cover F is ________. ------------------------------------------------------------------------------------------------------------------------------- Answer given 51 but why not 100?
asked Aug 23, 2018 in Linear Algebra srestha 361 views
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Boolean algebra is a bounded distributed complemented lattice, also lattice is a poset thus it satisfies reflexive , antisymmetric and transitive properties. Does Boolean Algebra satisfy commutative law?
asked Aug 22, 2018 in Mathematical Logic Nidhi Budhraja 354 views
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Ans. C
asked Aug 19, 2018 in Mathematical Logic Na462 433 views
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Determine whether each of these posets is well-ordered. (Q ∩[0, 1], ≤) (the set of rational numbers between 0 and 1 inclusive) The answer is not well ordered because as it doesn't have any unique least element as 0 can be expressed in p/q forms like (0/12,0/23,0/234). All are representing zero but there is no unique among them. Is this the reason here? Please confirm
asked Aug 15, 2018 in Set Theory & Algebra Abhijit Sen 4 139 views
1 vote
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Is below diagram is distributive lattice?
asked Jun 9, 2018 in Set Theory & Algebra srestha 2.3k views
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https://gateoverflow.in/27341/tifr2014-b-16z In this question, why ($\mathbb{N},∣)$ is not a complete lattice? For $any \ finite$ subset of $\mathbb{N}$, $LCM$ of its elements will be $lub$ and $HCF$ will be $glb$ and these $LCM$ and $HCF$ will also ... not complete lattice? The only reason I could come up with is they might not considering $0 \ \epsilon \ \mathbb{N}$. Is there any other reason?
asked Jun 8, 2018 in Set Theory & Algebra Soumya29 295 views
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Suppose Given a lattice i need to find how many pairs are there which will satisfy distributive property even though the given lattice is not distributive(becasue there exist atleast 1 element which has more than 1 complement ). How to solve such question. Say for example :-
asked May 31, 2018 in Set Theory & Algebra Na462 259 views
4 votes
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THEOREM:- The Poset $[D_{n};/] $ is a boolean algebra iff 'n' is a square-free number. If the Poset $[D_{n};/] $ is a boolean algebra then compliment of $x = \dfrac{n}{x}\: \forall x\in D_{n}$ Please explain this theorem?? and following question Q)Which of the following is not a boolean algebra?? $ A) [ D_{110};/ ] $ $ B) [ D_{91};/ ] $ $ C) [ D_{45};/ ]$ $ D) [ D_{64};/ ]$
asked Mar 19, 2018 in Set Theory & Algebra Lakshman Patel RJIT 2.7k views
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3 answers
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Q)which of the following is not a distributive lattice? a) [P(A);$\preceq$ ] where A = { a,b,c,d } b) [ {1,2,3,5,30} ; / ]
asked Mar 17, 2018 in Set Theory & Algebra Lakshman Patel RJIT 1.1k views
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3. A partially ordered set is said to be a lattice if every two elements in the set have (A) a unique least upper bound (B) a unique greatest lower bound (C) both (A) and (B) (D) none of the above
asked Feb 4, 2018 in Set Theory & Algebra kavikeve 741 views
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