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Recent questions tagged partial-order

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 4
Let $A$ be the set of all ordered pairs of integers, that is, $A=Z \times Z$. Define a binary relation $R$ on $A$ as follows: for all $(a, b),(c, d) \in A$ ... reflexive? Is $R$ symmetric? Is $R$ antisymmetric? Is $R$ transitive? Is $R$ an equivalence relation, a partial order, neither, or both?

GO Classes asked in Set Theory & Algebra 3 days ago

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 6
Let $A$ be any set. Subset Relation on $\mathrm{P}(\mathrm{A})$ is Anti-symmetric?

GO Classes asked in Set Theory & Algebra 3 days ago

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 8
Consider the following binary relations on the naturals (non-negative integers). Which ones are reflexive? Symmetric? Anti-symmetric? Transitive? Partial orders? Justify your claims. $A(x, y)$, defined to be true if and only if $y$ ... because eight comes before eighty-one, and $E(8,8)$ is true because eight comes no later than eight.)

GO Classes asked in Set Theory & Algebra 3 days ago

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 10
Are the following relations reflexive, symmetric, transitive, antisymmetric? Explain. Let $R$ be a relation on $\mathbb{Z}$ such that $(a, b) \in R$ iff $b=a$ or $b=-a$. Let $R$ be a relation on $\mathbb{R}$ ... $(a, b) \in R$ iff $a+b$ is a rational number, that is can be represented by a fraction.

GO Classes asked in Set Theory & Algebra 3 days ago

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 12
Define the binary relation $R$ on the set $A:=\{-4,-3,-2,-1,1,2,3,4\}$ as follows: $ (x, y) \in R \Longleftrightarrow\left|x^2-y^2\right| \leqslant 5 $ for all $x, y \in A$. Which of the following statements ... at all. $R$ is reflexive. $R$ is irreflexive. $R$ is transitive. $R$ is symmetric. $R$ is asymmetric. $R$ is antisymmetric.

GO Classes asked in Set Theory & Algebra 3 days ago

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 13
$ R=\left\{(x, y) \in \mathbb{N}^2: \exists n \in \mathbb{N}, x^n=y\right\} $ is a binary relation on the set of natural numbers $\mathbb{N}$. Determine which of the following properties ... symmetric Transitive For each property, either justify that the property always holds or show by a counterexample that the property does not hold.

GO Classes asked in Set Theory & Algebra 3 days ago

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 14
Determine if each of the following relations is reflexive, symmetric, antisymmetric, or transitive. Indicate if the relation is an equivalence relation. $R_1=\{(a, b) \mid-1 \leq a-b \leq 1\}$ on $\mathbf{R}$ ... $\mathbf{N}$ $ R_7=\left\{(a, b) \mid \frac{a}{b} \in \mathbf{Z}\right\}$ on $\mathbf{Z}$

GO Classes asked in Set Theory & Algebra 3 days ago

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 15
Let $R \subseteq \mathbb{N} \times \mathbb{N}$ be a relation ( $a$ binary relation) on the set of natural numbers defined as follows: $ (x, y) \in R \Leftrightarrow x+y \geq 18 \text {. } $ is $R$ reflexive ... . is R symmetric? Prove your answer. Is $R$ antisymmetric? Prove your answer. Is $\mathrm{R}$ transitive? Prove your answer.

GO Classes asked in Set Theory & Algebra 3 days ago

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 16
Among reflexive, symmetric, antisymmetric, and transitive, which of those properties are true of the above relation? It is both reflexive and symmetric It is only reflexive It is only antisymmetric It is both reflexive and transitive

GO Classes asked in Set Theory & Algebra 3 days ago

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 17
Among reflexive, symmetric, antisymmetric, and transitive, which of those properties are true of the above relation? It is both symmetric and transitive It is both reflexive and transitive It is reflexive, antisymmetric, and transitive It is both reflexive and antisymmetric

GO Classes asked in Set Theory & Algebra 3 days ago

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 18
Among reflexive, symmetric, antisymmetric, and transitive, which of those properties are true of the above relation? It is only reflexive It is reflexive, symmetric, and transitive It is both reflexive and antisymmetric It is both reflexive and symmetric

GO Classes asked in Set Theory & Algebra 3 days ago

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 19
Among reflexive, symmetric, antisymmetric, and transitive, which of those properties are true of the above relation? It is only transitive It is both antisymmetric and transitive It is both reflexive and transitive It has none of those properties

GO Classes asked in Set Theory & Algebra 3 days ago

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 22
Given the relation $R=\{(n, m)|n, m \in \mathbb{Z}| n,|\neq| m \mid\}$. Which of the following statements about $R$ is correct? $R$ is not an equivalence relation because it is not reflexive or ... relation because it is not antisymmetric $R$ is not an equivalence relation because it is not symmetric $R$ is an equivalence relation

GO Classes asked in Set Theory & Algebra 3 days ago

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 23
Determine whether the following relations are reflexive, symmetric, antisymmetric, and/or transitive: The empty relation $\text{R}=\{\}$ is defined on the natural numbers. The complete relation $\mathrm{R}=\mathbf{N} \times \mathbf{N}$ defined on the ... $\mathrm{R}$ on the integers where $a\text{R}b$ means $a^2=b^2$.

GO Classes asked in Set Theory & Algebra 3 days ago

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GO Classes 2023 | IIITH Mock Test 2 | Question: 53
A binary relation $\text{R}$ on a set $\text{A}$ is called connected iff for all elements $x$ and $y$ of $\text{A},$ either $x \text{R} y$ or $y \text{R} x.$ ... is/are true? Every connected relation is reflexive. Every connected relation is partial order. Every connected relation is symmetric. Every connected relation is transitive.

GO Classes asked in Set Theory & Algebra Apr 8

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GO Classes 2023 | IIITH Mock Test 1 | Question: 2
Given a set of values $\text{R} = \{1,2,3,4,5,6,7\}.$ The number of relations on this set which are both partial-order and equivalence relation is? $128$ $1$ $0$ $2^{42}$

GO Classes asked in Set Theory & Algebra Mar 26

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DRDO CSE 2022 Paper 1 | Question: 8
Given a powerset $S$ of $\{1,2,3\}$, its partial order $\leq$ is given by set inclusion. That is, for any subsets $T_{1} \neq T_{2}$ of $\{1,2,3\}$ we have $T_{1} \leq T_{2}$ if and only if $T_{1} \subset T_{2}$. Construct the Hasse diagram on $S$ under this partial order definition.

admin asked in Set Theory & Algebra Dec 15, 2022

by admin

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DRDO CSE 2022 Paper 1 | Question: 20
A partially ordered set $S=(\{3,4,12,24,48,72\}, /)$ is a _________ with _________ cycle$(s).$

admin asked in Set Theory & Algebra Dec 15, 2022

by admin

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Best Open Video Playlist for Partial Orders and Lattices Topic | Discrete Mathematics
Please list out the best free available video playlist for Partial Orders and Lattices Topic from Discrete Mathematics as an answer here (only one playlist per answer). We'll then select the best playlist and add ... ones are more likely to be selected as best. For the full list of selected videos please see here

makhdoom ghaya asked in Study Resources Aug 15, 2022

by makhdoom ghaya

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2 votes

1 answer

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GO Classes Weekly Quiz 10 | Discrete Mathematics | Set Theory, Mathematical Logic, Lattice | Question: 4

GO Classes asked in Set Theory & Algebra May 12, 2022

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3 votes

1 answer

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GO Classes Weekly Quiz 10 | Discrete Mathematics | Set Theory, Mathematical Logic, Lattice | Question: 5

GO Classes asked in Set Theory & Algebra May 12, 2022

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2 votes

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GO Classes Weekly Quiz 10 | Discrete Mathematics | Set Theory, Mathematical Logic, Lattice | Question: 6

GO Classes asked in Set Theory & Algebra May 12, 2022

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GO Classes Weekly Quiz 10 | Discrete Mathematics | Set Theory, Mathematical Logic, Lattice | Question: 7

GO Classes asked in Set Theory & Algebra May 12, 2022

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4 votes

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GO Classes Weekly Quiz 10 | Discrete Mathematics | Set Theory, Mathematical Logic, Lattice | Question: 13

GO Classes asked in Set Theory & Algebra May 12, 2022

333 views

4 votes

2 answers

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GO Classes Weekly Quiz 10 | Discrete Mathematics | Set Theory, Mathematical Logic, Lattice | Question: 14

GO Classes asked in Set Theory & Algebra May 12, 2022

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Recent questions tagged partial-order