# Recent questions tagged lattice

1
Let $L$ be a lattice. Then for every $a$ and $b$ in $L$ which one of the following is correct? $a\lor b = a​\land \:b$ $a\lor(b\lor c)=(a\lor b)\lor c$ $a\lor(b​\land \:c)=a$ $a\lor(b\lor c)=b$
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what is the least upper bound of {a, b, c}?
1 vote
3
The number of totally ordered set compatible to the given POSET are __________
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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 .
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What is dual of a POSET?
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Can a countable infinite lattice be bounded?
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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?
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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?
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I am getting 3 minimal please check it
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My doubt is in second hasse diagram for (I,g) lub should be I and j so it is not lattice please correct me if i amwrong
1 vote
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Prove that every complete lattice is bounded lattice but not vice-versa .
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Is 1 a lattice?
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What is dual of a lattice? Also give an example
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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?
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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?
1 vote
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Ans. C
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What will be lower bound of {g}
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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
1 vote
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Is below diagram is distributive lattice?
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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?
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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 :-
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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?? $A) [ D_{110};/ ]$ $B) [ D_{91};/ ]$ $C) [ D_{45};/ ]$ $D) [ D_{64};/ ]$
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} ; / ]