All Questions
Tagged with lattice-orders relations
36
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Show that the set of all partitions of a set S with the relation refinement is a lattice.
This one may be one duplicate of QA_1, but its example $\{\{a,d\},\{b,c\}\}\wedge\{\{a\},\{b,c,d\}\}$ seems to not meet the definition in the book because $(\{a,d\} \not\subseteq \{a\}) \wedge (\{a,d\}...
- 416
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34
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Prove equivalence between properties of relations using fixpoint calculus
The problem
Let $a$ be a binary endorelation of some countable set $S$, i.e. $a \subseteq S \times S$ .
I need to show that the following properties are equivalent:
$ (a^*)^{-1} ; a^* \subseteq a^* ; ...
- 550
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1
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$P$ be a poset and $X, Y \subseteq P$. Is it true that if $\downarrow X = \downarrow Y$ , then $X= Y$?
Let $P$ be a poset and $X, Y \subseteq P$. Is it true that if $\downarrow X = \downarrow Y$ (the generated down-sets) then $X= Y$?
I must show that when $\forall x \in X \,\,\exists \,\, y\in Y$ s.t $...
- 1,133
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Difference between total order and linear order
I want to ask a clarificatory doubt. I am really confused with the two definitions of linear order. In one definition it is said to be same as total order but in the other definition it is irreflexive ...
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What is this equivalence relation on the elements of a lattice?
Suppose I have a lattice, and I pick one of its elements $a$. Then I define a relation on all elements of the lattice by
$$x \sim_a y \iff x \vee a = y \vee a.$$
In other words, two elements are ...
- 371
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2
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Is this ordered set a Lattice?
So I have this problem:
Let $S$ be the set of all reflexive, symmetric relations on $\mathbb N$, $A$ the set of all reflexive antisymmetric relations on $\mathbb N$. Now consider the set $M=S\cup A$. ...
- 125
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Determining whether a lattice is complemented
Determine whether the lattice below is a complemented lattice:
I'm currently struggling with a problem relating to a lattice that is very similar to the lattice above.
The above lattice is a bounded ...
- 249
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1
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105
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Is the relation "x is a subset of y" on the powerset $P(S)$ of a finite set $S$ a lattice?
Is the relation "x is a subset of y" on the power set $P(S)$ of a finite set $S$ a lattice? My professor asked this question.
We defined in class , a lattice , a set of elements, where ...
- 829
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177
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Smallest lattice which is a boolean algebra can contain only one element?
if we have ({1},>=)
then 1>=1 therefore reflexive ,anti-symmetric as (1,1) ,transitive . so it is a POSET and 1^1=1 and again 1LUB1=1 so 1 is the complement of itself the set has LUB and GLB for ...
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508
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Is every finite lattice also complete?
I have to proof the every finite lattice is also a complete lattice but I'dont known where to start.
From definition, a lattice is a poset in which every pair of elements has a least upper bound and ...
- 1
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Prove that Multiset and relation $\preccurlyeq$ is a lattice ($\preccurlyeq$ is defined like $\leq$)
Multiset is a set that can have more than one of each member for example $\{1,3,3,9\}$ is a Multiset. Let $\mathbb{K}$ be the set of all multisets that has exactly $k$ members. ($k$ is a fixed ...
- 749
2
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236
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Any order preserving map of a poset into itself has a fixed point
In the book of Algebra by Hungerford, at pafe 15, it is claimed that
However, consider $(\mathbb{R}, \leq)$ and $f: \mathbb{R} \to \mathbb{R}$ defined by $f(x)=x+1$. It is a complete partially ...
- 7,337
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2
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Is every subset of a lattice a lattice?
Is every subset of a lattice a lattice?
Lattice consists of a partially ordered set in which every two elements have to have unique supremum and infimum.
I'm confused about what the answer is. I ...
- 389
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1
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751
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Quickly determining whether given lattice is a distributive lattice from a given Hasse diagram
I came across following fact while reading online:
If a given Hasse diagram contains following structures, then it wont be the distributive lattice
I am unsure if the above fact is correct and ...
- 1,317
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How to identify if a given Hasse diagram is a lattice [closed]
How to identify if a given Hasse diagram is a lattice?
user521804