Recent questions tagged equivalence-class / GATE Overflow for GATE CSE

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Discrete Mathematics | Set Theory | Relation | Equivalance Relation
which if the following statement is True for every set? a. $\exists$ a equivalence class that is also a partition set. b. Every equivalence relation on a set defines a partition of that set. c. $\exists$ a partition of a set that is also equal to equivalence class of the set on some equivalence relation.

which if the following statement is True for every set?a. $\exists$ a equivalence class that is also a partition set.b. Every equivalence relation on a set defines a part...

RahulVerma3

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RahulVerma3 asked Apr 12

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2

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 ?

RahulVerma3

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RahulVerma3 asked Mar 30

4 votes

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3

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...

GO Classes

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GO Classes asked Jan 28

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Discrete math

Çșȇ ʛấẗẻ

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Çșȇ ʛấẗẻ asked Sep 14, 2023

14 votes

3 answers

5

GATE CSE 2023 | Question: 39
Let $f: A \rightarrow B$ be an onto (or surjective) function, where $A$ and $B$ are nonempty sets. Define an equivalence relation $\sim$ on the set $A$ as \[ a_{1} \sim a_{2} \text { if } f\left(a_{1}\right)=f\left(a_{2}\right), \] ... is NOT well-defined. $F$ is an onto (or surjective) function. $F$ is a one-to-one (or injective) function. $F$ is a bijective function.

Let $f: A \rightarrow B$ be an onto (or surjective) function, where $A$ and $B$ are nonempty sets. Define an equivalence relation $\sim$ on the set $A$ as\[a_{1} \sim a_{...

admin

5.9k views

admin asked Feb 15, 2023

4 votes

1 answer

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GO Classes Test Series 2023 | Theory of Computation | Test 2 | Question: 10
Let $\text{L}$ be a language over an alphabet $\Sigma$. The equivalence relation $\sim_{\text{L}}$ on the set $\Sigma^{\ast}$ of finite strings over $\Sigma$ ... $1$ Only $2$ Both None

Let $\text{L}$ be a language over an alphabet $\Sigma$. The equivalence relation $\sim_{\text{L}}$ on the set $\Sigma^{\ast}$ of finite strings over $\Sigma$ is defined b...

GO Classes

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GO Classes asked Jun 22, 2022

7 votes

1 answer

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GO Classes Test Series 2024 | Discrete Mathematics | Test 2 | Question: 16
Let $\text{Z}$ be the set of all integers. Define a relation $\text{S}$ on $\text{Z} \times \text{Z}$ by $(w,x)\text{S}(y,z)$ if and only if $w-x = y-z.$ We know that $\text{S}$ is an equivalence relation. Which of the ... class of $(a,b)$ is disjoint from the equivalence class of $(a-2,b+2),$ for all $a,b,c,d \in \text{Z}.$

Let $\text{Z}$ be the set of all integers. Define a relation $\text{S}$ on $\text{Z} \times \text{Z}$ by $(w,x)\text{S}(y,z)$ if and only if $w-x = y-z.$ We know that $\t...

GO Classes

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GO Classes asked Apr 21, 2022

3 votes

1 answer

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GO Classes 2023 | Weekly Quiz 7 | Question: 12
Let $\text{A, B}$ be two non-empty sets, with cardinality $3,4$ respectively. Let $\text{R}$ be a relation defined on the power set of $\text{A} \times \text{B}.$ Relation $\text{R}$ is reflexive, symmetric, transitive and antisymmetric. How many equivalence classes does relation $\text{R}$ have?

Let $\text{A, B}$ be two non-empty sets, with cardinality $3,4$ respectively. Let $\text{R}$ be a relation defined on the power set of $\text{A} \times \text{B}.$ Relatio...

GO Classes

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GO Classes asked Apr 14, 2022

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1 answer

9

ZEAL test-series : Cardinality of relation!
I know that the number of equivalence relation is bell no. i.e 7th bell no. i.e. 877, but i am not able to find the cardinality of R! Please help!

I know that the number of equivalence relation is bell no. i.e 7th bell no. i.e. 877, but i am not able to find the cardinality of R!Please help!

Yashdeep2000

709 views

Yashdeep2000 asked Mar 6, 2022

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1 answer

10

Rosen 7e Exercise-9.5 Question no-9 page no-615
Suppose that $A$ is a nonempty set, and $f$ is a function that has $A$ as its domain. Let $R$ be the relation on $A$ consisting of all ordered pairs $(x, y)$ such that $f (x)=f (y)$ $a)$ Show that $R$ is an equivalence relation on $A$ $b)$ What are the equivalence classes of $R?$

Suppose that $A$ is a nonempty set, and $f$ is a function that has $A$ as its domain. Let $R$ be the relation on $A$ consisting of all ordered pairs $(x, y)$ such that $f...

aditi19

1.3k views

aditi19 asked Apr 23, 2019

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11

finding equivalence classes $R_L$ of given languages and separating words
hello, i've just solved 2 questions among many, but i'm not sure i've got to the right result. could you check if i did it correctly(especially 2) as it's more complicated). both are over ... classes. could you help me with that please? thank you very much for your help, really hoping i did it correctly.

hello,i’ve just solved 2 questions among many, but i’m not sure i’ve got to the right result. could you check if i did it correctly(especially 2) as it’s more com...

csenoob

373 views

csenoob asked Dec 7, 2018

0 votes

1 answer

12

UGC NET CSE | July 2018 | Part 2 | Question: 89
Which of the following is an equivalence relation on the set of all functions from Z to Z? $\{ f, \:g) \mid f(x) - g(x) =1 \: \forall \: x \in \: Z \}$ $\{ f, \:g) \mid f(0) = g(0) \text{ or } f(1) = g(1) \}$ $\{ f, \:g) \mid f(0) = g(1) \text{ and } f(1) = g(0) \}$ $\{ f, \:g) \mid f(x) - g(x) =k \text{ for some } k \in Z \}$

Which of the following is an equivalence relation on the set of all functions from Z to Z?$\{ f, \:g) \mid f(x) - g(x) =1 \: \forall \: x \in \: Z \}$$\{ f, \:g) \mid f(0...

Pooja Khatri

868 views

Pooja Khatri asked Jul 13, 2018

1 votes

1 answer

13

Equivalence classes
Consider a regular language L over Σ={0,1} such that L contains every string which ends with "0". The number of equivalence classes in L is ______.

Consider a regular language L over Σ={0,1} such that L contains every string which ends with "0". The number of equivalence classes in L is ______.

Parshu gate

1.3k views

Parshu gate asked Nov 27, 2017

0 votes

0 answers

14

Equivalence Relation
Which of the above are true. I think only 1st one is true. But the answer given is all are true.

Which of the above are true.I think only 1st one is true. But the answer given is all are true.

Shubhanshu

459 views

Shubhanshu asked Nov 15, 2017

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