Recent questions tagged relations

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Finite Automata Combined with Relation
Let DFA , M = (Q, ∑, δ, q$_0$, F) and Relation R is defined on Q as R:Q$\rightarrow$Q such that pRq iff $\forall$ w ∈ $\Sigma$* [ δ*(p,w) ∈ F $\leftrightarrow$ δ*(p,w) ∈ F OR δ* (p, w) ∉ F $\leftrightarrow$ δ* (q, w) ∉ F] then ____________ A) R is Reflexive B) R is Symmetric C) R is transitive D) None

Let DFA , M = (Q, ∑, δ, q$_0$, F) and Relation R is defined on Q as R:Q$\rightarrow$Q such that pRq iff $\forall$ w ∈ $\Sigma$* [ δ*(p,w) ∈ F $\leftrightarrow$ δ...

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jaydip74 asked 1 day ago

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Discrete Mathematics | Relations | Equivalence relation |
The relation R on the set {(a, b) |a, b € Z} where (a, b)R(c, d) means a = c or b = d. Is R a equivalence relation or not ?

The relation R on the set {(a, b) |a, b € Z} where (a, b)R(c, d) means a = c or b = d. Is R a equivalence relation or not ?

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RahulVerma3 asked Mar 30

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GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 62
As a refresher, if $R$ is an equivalence relation over a set $A$ and $x \in A$, then the equivalence class of $\boldsymbol{x}$ in $\boldsymbol{R}$, denoted $[x]_R,$ is the set $ [x]_R=\{y \in A \mid x R y\} $ Let's now introduce some ... $\mathrm{I}(\mathrm{R})=n / 2$ and $\mathrm{W}(\mathrm{R})=n / 2$

As a refresher, if $R$ is an equivalence relation over a set $A$ and $x \in A$, then the equivalence class of $\boldsymbol{x}$ in $\boldsymbol{R}$, denoted $[x]_R,$ is th...

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GO Classes asked Jan 28

9 votes

1 answer

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GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 38
A binary relation $\mathrm{R}$ over a set $\mathrm{A}$ is called a "GO Relation" if for all $\mathrm{x}, \mathrm{y}, \mathrm{z}$ $\in A$, if $x R y$ and $x R z$, then $y R z$. Which of the following ... is transitive. If $R$ is a GO relation then $R$ is reflexive. If $R$ is an equivalence relation then $R$ is a GO relation.

A binary relation $\mathrm{R}$ over a set $\mathrm{A}$ is called a "GO Relation" if for all $\mathrm{x}, \mathrm{y}, \mathrm{z}$ $\in A$, if $x R y$ and $x R z$, then $y ...

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GO Classes asked Jan 13

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2 answers

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 1
Let $A=\{0,1,2,3\}$ and $R$ a relation over $A$ : $ R=\{(0,0),(0,1),(0,3),(1,1),(1,0),(2,3),(3,3)\} $ Draw the directed graph of $R$. Check whether $R$ is an equivalence relation. Give a counterexample in each case in which the relation does not satisfy one of the properties of being an equivalence relation.

Let $A=\{0,1,2,3\}$ and $R$ a relation over $A$ :$$R=\{(0,0),(0,1),(0,3),(1,1),(1,0),(2,3),(3,3)\}$$Draw the directed graph of $R$. Check whether $R$ is an equivalence re...

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GO Classes asked May 28, 2023

2 votes

1 answer

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 2
$\begin{array}{l|llllll} \textbf{Relations on}\; \mathbb{Z}: & \quad < & \qquad \leq & \qquad = & \qquad \mid & \qquad \nmid & \qquad \neq \\ \hline \hline \text{Reflexive} & \\ \text{Symmetric} & \\ \text{Transitive} & \end{array}$ Fill "Yes or No" in the above table.

$$\begin{array}{l|llllll}\textbf{Relations on}\; \mathbb{Z}: & \quad < & \qquad \leq & \qquad = & \qquad \mid & \qquad \nmid & \qquad \neq \\\hline \hline \text{Reflexive...

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GO Classes asked May 28, 2023

1 votes

2 answers

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 3
The following table describes a binary relation. Find the set of ordered pairs that is this relation, as in the definition of a binary relation. ...

The following table describes a binary relation. Find the set of ordered pairs that is this relation, as in the definition of a binary relation.$$\begin{array}{c|c|c|c|c|...

408 views

GO Classes asked May 28, 2023

1 votes

1 answer

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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?

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 $(a, b),(c, d) \in A$,$$(a, b) R(c, ...

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GO Classes asked May 28, 2023

2 votes

2 answers

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 5
Define $\mathcal{R}$ the binary relation on $\mathbb{N} \times \mathbb{N}$ to mean $(a, b) \mathcal{R}(c, d)$ iff $b \mid d$ and $a \mid c$ $\mathcal{R}$ is symmetric but not reflexive. $\mathcal{R}$ is transitive and symmetric but not reflexive $\mathcal{R}$ is reflexive and transitive but not symmetric None of the above

Define $\mathcal{R}$ the binary relation on $\mathbb{N} \times \mathbb{N}$ to mean $(a, b) \mathcal{R}(c, d)$ iff $b \mid d$ and $a \mid c$$\mathcal{R}$ is symmetric but ...

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GO Classes asked May 28, 2023

1 votes

1 answer

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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?

Let $A$ be any set. Subset Relation on $\mathrm{P}(\mathrm{A})$ is Anti-symmetric?

360 views

GO Classes asked May 28, 2023

1 votes

1 answer

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 7
Define $\mathcal{R}$ the binary relation on $\mathbb{N} \times \mathbb{N}$ to mean $(a, b) \mathcal{R}(c, d)$ iff $b \mid d$ and $a \mid c$

Define $\mathcal{R}$ the binary relation on $\mathbb{N} \times \mathbb{N}$ to mean $(a, b) \mathcal{R}(c, d)$ iff $b \mid d$ and $a \mid c$

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GO Classes asked May 28, 2023

1 votes

1 answer

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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.)

Consider the following binary relations on the naturals (non-negative integers). Which ones are reflexive? Symmetric? Anti-symmetric? Transitive? Partial orders? Justify ...

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GO Classes asked May 28, 2023

1 votes

1 answer

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 9
The relation $\mathcal{R}$ on $\mathbb{Q}$ with $\forall x, y \in \mathbb{Q}: x \sim y$ if $x y=0$. The relation "has the same mother" on the set of students. The relation $\sim$ on $\mathbb{Q}$ where $a, b \in \mathbb{Q}$ ... $\{a, b, c\}$. The relation $\{(x, x),(y, y)\}$ on $\{x, y\}.$

The relation $\mathcal{R}$ on $\mathbb{Q}$ with $\forall x, y \in \mathbb{Q}: x \sim y$ if $x y=0$.The relation "has the same mother" on the set of students.The relation ...

267 views

GO Classes asked May 28, 2023

1 votes

1 answer

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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.

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 $b=-a$.Le...

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GO Classes asked May 28, 2023

1 votes

1 answer

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 11
Let $A \neq \varnothing$ be a set. Consider the following statements: $\varnothing$ is a reflexive binary relation on $A$; $\varnothing$ is a symmetric binary relation on $A ;$ $\varnothing$ is a transitive binary relation on $A$; Which of ... $(2)$ are correct. Only $(2)$ and $(3)$ are correct. None is correct. All are correct.

Let $A \neq \varnothing$ be a set. Consider the following statements:$\varnothing$ is a reflexive binary relation on $A$;$\varnothing$ is a symmetric binary relation on $...

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GO Classes asked May 28, 2023

1 votes

1 answer

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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.

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 $x, y \in A$...

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GO Classes asked May 28, 2023

1 votes

1 answer

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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.

$$R=\left\{(x, y) \in \mathbb{N}^2: \exists n \in \mathbb{N}, x^n=y\right\}$$is a binary relation on the set of natural numbers $\mathbb{N}$.Determine which of the follow...

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GO Classes asked May 28, 2023

1 votes

1 answer

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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 $\mathbf{Z}$

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...

420 views

GO Classes asked May 28, 2023

1 votes

1 answer

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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.

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 \g...

298 views

GO Classes asked May 28, 2023

1 votes

1 answer

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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

Among reflexive, symmetric, antisymmetric, and transitive, which of those properties are true of the above relation?It is both reflexive and symmetricIt is only reflexive...

270 views

GO Classes asked May 28, 2023

1 votes

2 answers

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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

Among reflexive, symmetric, antisymmetric, and transitive, which of those properties are true of the above relation?It is both symmetric and transitiveIt is both reflexiv...

386 views

GO Classes asked May 28, 2023

1 votes

1 answer

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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

Among reflexive, symmetric, antisymmetric, and transitive, which of those properties are true of the above relation?It is only reflexiveIt is reflexive, symmetric, and tr...

362 views

GO Classes asked May 28, 2023

1 votes

1 answer

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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

Among reflexive, symmetric, antisymmetric, and transitive, which of those properties are true of the above relation?It is only transitiveIt is both antisymmetric and tran...

269 views

GO Classes asked May 28, 2023

1 votes

1 answer

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 20
Let $R$ be the relation on $M=\{1,2,3\}$ with the following diagraph representation: Then $R$ is not reflexive, not symmetric, and not transitive $R$ is transitive but not reflexive $R$ is an equivalence relation $R$ is symmetric but not transitive $R$ is reflexive but not symmetric

Let $R$ be the relation on $M=\{1,2,3\}$ with the following diagraph representation:Then$R$ is not reflexive, not symmetric, and not transitive$R$ is transitive but not r...

330 views

GO Classes asked May 28, 2023

2 votes

1 answer

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 21
Define the relation $\mathrm{O}$ on $\mathrm{Z}$ as follows: $ \forall m, n \in Z, m O n \longleftrightarrow \exists k \in Z \mid(m-n)=2 k+1 $ ... $\mathrm{O}$ is not reflexive, symmetric, and not transitive.

Define the relation $\mathrm{O}$ on $\mathrm{Z}$ as follows:$$\forall m, n \in Z, m O n \longleftrightarrow \exists k \in Z \mid(m-n)=2 k+1$$Which one of the following st...

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GO Classes asked May 28, 2023

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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

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 ...

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GO Classes asked May 28, 2023

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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 $a^2=b^2$.

Determine whether the following relations are reflexive, symmetric, antisymmetric, and/or transitive:The empty relation $\text{R}=\{\}$ is defined on the natural numbers....

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GO Classes asked May 28, 2023

1 votes

1 answer

28

GO Classes Set Theory And Algebra Practice Set 1 | Question: 24
For each of the following relations $R$ on the set of real numbers, decide whether it is reflexive, symmetric, and/or transitive? Justify your arguments. Is the relation an equivalence relation? Explain. $(x, y) \in R$ if and only if $|x-y| \leq 3$ ... $(x, y) \in R$ if and only if $|x+y|=|x|+|y|$.

For each of the following relations $R$ on the set of real numbers, decide whether it is reflexive, symmetric, and/or transitive? Justify your arguments. Is the relation ...

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GO Classes asked May 28, 2023

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