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Recent questions tagged equivalence-class

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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 $\mathrm{W}(\mathrm{R})=n / 2$

GO Classes asked in Set Theory & Algebra Jan 28

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Çșȇ ʛấẗẻ asked in Algorithms Sep 14, 2023

by Çșȇ ʛấẗẻ

79 views

11 votes

2 answers

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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.

admin asked in Set Theory & Algebra Feb 15, 2023

by admin

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4 votes

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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

GO Classes asked in Theory of Computation Jun 22, 2022

381 views

6 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 $a,b,c,d \in \text{Z}.$

GO Classes asked in Set Theory & Algebra Apr 21, 2022

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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?

GO Classes asked in Set Theory & Algebra Apr 14, 2022

684 views

0 votes

1 answer

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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!

Yashdeep2000 asked in Set Theory & Algebra Mar 6, 2022

by Yashdeep2000

668 views

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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 $R?$

aditi19 asked in Set Theory & Algebra Apr 23, 2019

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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.

csenoob asked in Theory of Computation Dec 7, 2018

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1 answer

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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? $\{ f, \:g) \mid f(x) - g(x) =1 \: \forall \: x \in \: Z \}$ $\{ f, \:g) \mid f(0) = g(0) \text{ or } f(1) = g(1) \}$ $\{ f, \:g) \mid f(0) = g(1) \text{ and } f(1) = g(0) \}$ $\{ f, \:g) \mid f(x) - g(x) =k \text{ for some } k \in Z \}$

Pooja Khatri asked in Discrete Mathematics Jul 13, 2018

by Pooja Khatri

849 views

1 vote

1 answer

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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 ______.

Parshu gate asked in Theory of Computation Nov 27, 2017

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

Shubhanshu asked in Set Theory & Algebra Nov 15, 2017

450 views

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Equivalence relation
True / false ? a. Partitions formed from congruence classes modulo $6$ ... $R_4$ creates refinement partitions with respect to the partitions of $R_3$.

dd asked in Set Theory & Algebra Dec 14, 2016

by dd

501 views

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Gate Computer Science group Fb post

Shreya Roy asked in Set Theory & Algebra Nov 28, 2016

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Recent questions tagged equivalence-class