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151

Is the given relation transitive
For given R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(3,4),(4,3)} Is the given relation transitive?

sripo asked in Set Theory & Algebra Oct 6, 2018

by sripo

391 views

0 votes

2 answers

152

Recurrence Relation
Let $T(n) = T(n-1) + \frac{1}{n} , T(1) = 1 ;$ then $T(n) = ? $ $O(n^{2})$ $O(logn)$ $O(nlogn)$ $O(n^{2}logn)$

Lakshman Bhaiya asked in Combinatory Oct 5, 2018

by Lakshman Bhaiya

1.4k views

0 votes

1 answer

153

Relation
State True or False? Empty set Φ is an equivalence relation.

srestha asked in Set Theory & Algebra Sep 21, 2018

1.9k views

1 vote

1 answer

154

ISI2017-PCB-A-3
Let $B=\{1, 2, 3, 4\}$. A set $S \subseteq B \times B$ called a symmetric set of $B$ if for all $x, y \in B$, $ (x, y) \in S \Rightarrow (y,x) \in S.$ Find the number of symmetric sets of $B$.

go_editor asked in Set Theory & Algebra Sep 19, 2018

473 views

0 votes

1 answer

155

Relations
What is the smallest binary relation possible from A to B? Is it Null Set? If so, how is it possible relations are subsets of AxB (cartesian product) and if AxB is not supposed to be containing a Null Set.

superak96 asked in Set Theory & Algebra Aug 22, 2018

458 views

0 votes

1 answer

156

State True/False
1. If f is bijective function then f-1 is also bijective function. 2. If f is surjective function then f-1 is a function but not surjective. 3. Inverse of a function 'f' is a function only when it is bijective. 4. If a relation R: X->Y is left total, then it must be a function.

Naveen Kumar 3 asked in Set Theory & Algebra Aug 17, 2018

by Naveen Kumar 3

1.2k views

0 votes

0 answers

157

Kenneth Rosen Edition 6th Exercise 7.6 Question 54 (Page No. 525)
Determine whether each of these posets is well-ordered. (Q ∩[0, 1], ≤) (the set of rational numbers between 0 and 1 inclusive) The answer is not well ordered because as it doesn't have any unique least element as 0 ... 23,0/234). All are representing zero but there is no unique among them. Is this the reason here? Please confirm

Abhijit Sen 4 asked in Set Theory & Algebra Aug 14, 2018

by Abhijit Sen 4

517 views

13 votes

4 answers

158

GATE CSE 1998 | Question: 10b
Let $R$ be a binary relation on $A = \{a, b, c, d, e, f, g, h\}$ represented by the following two component digraph. Find the smallest integers $m$ and $n$ such that $m < n$ and $R^m = R^n$.

Arjun asked in Set Theory & Algebra Aug 12, 2018

by Arjun

4.2k views

0 votes

1 answer

159

Doubt
Is empty relation an equivalence relation?

aditi19 asked in Set Theory & Algebra Aug 4, 2018

231 views

3 votes

3 answers

160

Test Series
Examine the structure of the EMPLOYEES table: EMPLOYEE_ID NUMBER Primary Key FIRST_NAME VARCHAR2(25) LAST_NAME VARCHAR2(25) Assume all the following four options are executed in the same sequence order. Which statement will not insert a row into the table? a. INSERT ... (employee_id) VALUES (1000); d. INSERT INTO employees (employee_id, first_name, last_name) VALUES ( 1000, John', ');

Subham Nagar asked in Databases Aug 1, 2018

by Subham Nagar

12.5k views

0 votes

1 answer

161

Kenneth Rosen Edition 6th Exercise 7.4 Example 7 (Page No. 493)
I am not getting the (2n-1) factor. n^2 is for matrix mul and multiplication is being done (n-1) times. so n^2(n-1) is understood. But what is (2n-1)??

tusharp asked in Set Theory & Algebra Jul 14, 2018

439 views

0 votes

2 answers

162

UGC NET CSE | July 2018 | Part 2 | Question: 88
Which of the relations on {0, 1, 2, 3} is an equivalence relation? { (0, 0) (0, 2) (2, 0) (2, 2) (2, 3) (3, 2) (3, 3) } { (0, 0) (1, 2) (2, 2) (3, 3) } { (0, 0) (0, 1) (0, 2) (1, 0) (1, 1) (1, 2) (2, 0) } { (0, 0) (0, 2) (2, 3) (1, 1) (2, 2)

Pooja Khatri asked in Discrete Mathematics Jul 13, 2018

by Pooja Khatri

3.1k views

1 vote

0 answers

163

Kenneth Rosen Edition 6th Exercise 7.6 Question 60 b (Page No. 511)
Let R be the relation on the set of functions from $Z^+$ to itself such that (f,g) belongs to R iff f is $\Theta(g)$ The equivalence class of f(n)=$n^2$ is set of all functions who are in $\Theta(n^2)$ is it correct?

Ayush Upadhyaya asked in Set Theory & Algebra Jun 30, 2018

by Ayush Upadhyaya

250 views

1 vote

0 answers

164

Kenneth Rosen Edition 6th Exercise 7.5 Question 57 (Page No. 509)
Consider the equivalence relation R = $\{(x,y) \, | \, x-y \,is\,an\,integer\}$ (b) What is the equivalence class of 1/2 for this equivalence relation?

Ayush Upadhyaya asked in Set Theory & Algebra Jun 30, 2018

by Ayush Upadhyaya

525 views

1 vote

0 answers

165

Kenneth Rosen Edition 6th Exercise 7.5 Question 35 (Page No. 508)
What is the congruence class $[n_5]$ (that is, the equivalence class of n with respect to congruence modulo 5) when n is 6 I think it would be like $[6]_{5} \equiv[1]_5$ which is set of all numbers which leave a remainder of 1 ... 5. but in rosen answer is given in format $\{i\, \equiv 6mod5\}$ So is my answer same as given in text?

Ayush Upadhyaya asked in Set Theory & Algebra Jun 30, 2018

by Ayush Upadhyaya

319 views

0 votes

0 answers

166

Kenneth Rosen Edition 6th Exercise 7.4 Question 2 (Page No. 497)
Let R be the relation $\{(a,b)\, |\, a\not= b\}$ on the set of integers. What is the reflexive closure of R? As per my analysis, the matrix of this relation would have 1's everywhere except on ... the smallest relation containing R that is both symmetric and reflexive, then is the reflexive closure of R answer to this problem?

Ayush Upadhyaya asked in Set Theory & Algebra Jun 30, 2018

by Ayush Upadhyaya

374 views

0 votes

1 answer

167

Kenneth Rosen Edition 6th Exercise 7.1 Question 44 (Page No. 473)
Let $S$ be a set with $n$ elements and let $a$ and $b$ be distinct elements of $S$. How many relations are there on $S$ such that (a) $(a,b) \in S$ (b) $(a,b) \not\in S$ (c) There are no ordered pairs in the relation that have "$a$" ... $2^{(n-1)^2}$ (f) $2^{n^2}-2^{(n-1)^2}$ Please let me know if my work is correct.

Ayush Upadhyaya asked in Set Theory & Algebra Jun 29, 2018

by Ayush Upadhyaya

2.0k views

1 vote

2 answers

168

Kenneth Rosen Edition 6th Exercise 7.1 Question 35 (Page No. 473)
Let $R_1,R_4,R_6$ be relations on the set of real numbers to the set of real numbers $R_1=\{(a,b) \in R^2 \, | \, a>b\}$ $R_4=\{(a,b) \in R^2\, | \, a \leq b\}$ $R_6=\{(a,b) \in R^2 \, | \, a \neq b\}$ Find (d) $R_4 o R_1$ (g)$R_4 o R_6$

Ayush Upadhyaya asked in Set Theory & Algebra Jun 29, 2018

by Ayush Upadhyaya

557 views

1 vote

1 answer

169

Kenneth Rosen Edition 6th Exercise 7.1 Question 48 (Page No. 473)
Suppose that $R$ and $S$ are reflexive relations on a set A.Are the below statements true or false? (a) $R\, \cup \, S$ is reflexive (b)$R\, \cap \, S$ is reflexive (c)$R\, \oplus \, S$ is irreflexive (d)$R\, - \, S$ is irreflexive (e)$SoR$ is reflexive. My Answers are (a)-(e)-All true. Are my answers correct?

Ayush Upadhyaya asked in Set Theory & Algebra Jun 29, 2018

by Ayush Upadhyaya

1.6k views

0 votes

0 answers

170

Kenneth Rosen Edition 6th Exercise 7.1 Question 7 (Page No. 472)
Given below is a table where R is a relation having pairs (x,y) over the set of Integers and these ordered pairs will be in R if and only if the condition given on the left most side of the table is ... -Reflexive IR-Irreflexive S-Symmetric ATS-Anti-symmetric AS-Asymmetric T-Transitive. Let me know if below table entries are correct.

Ayush Upadhyaya asked in Set Theory & Algebra Jun 29, 2018

by Ayush Upadhyaya

577 views

0 votes

0 answers

171

Kenneth Rosen Edition 6th Exercise 7.1 Question 6 (Page No. 471)
Given below is a table where R is a relation having pairs (x,y) over the set of real numbers and these ordered pairs will be in R if and only if the condition given on the left most side of the table ... -Reflexive IR-Irreflexive S-Symmetric ATS-Anti-symmetric AS-Asymmetric T-Transitive. Let me know if below table entries are correct.

Ayush Upadhyaya asked in Set Theory & Algebra Jun 29, 2018

by Ayush Upadhyaya

549 views

0 votes

1 answer

172

Quasi- Order Relations
What are the conditions for a relation to be quasi-ordered? In NPTEL video lectures, I found conditions for it to be Irreflexive and Transitive. But on Wikipedia and other resources, it's given that a binary relation R on a set A quasi-order if it is Reflexive and Transitive. Which one is correct ? or Am I missing something?

Soumya29 asked in Set Theory & Algebra Jun 6, 2018

896 views

3 votes

1 answer

173

Problem in gate1998-10 part b -
Can someone help me in "part b" of this question- https://gateoverflow.in/1724/gate1998-10 . I am still not able to understand why $R^0$ is considered here ? and what is $R^0 $? Is it Equality relation? Do we have to consider it in every question of this type ?

Soumya29 asked in Set Theory & Algebra May 22, 2018

1.2k views

5 votes

2 answers

174

CMI2015-A-02
A binary relation $R ⊆ (S S)$ is said to be Euclidean if for every $a, b, c ∈ S, (a, b) ∈ R$ and $(a, c) ∈ R$ implies $(b, c) ∈ R$. Which of the following statements is valid? If $R$ is Euclidean, $(b, a) ∈ R$ and $(c, a) ∈ R$, then $(b, c) ∈ R$ ... $R$ is Euclidean, $(a, b) ∈ R$ and $(b, c) ∈ R$, then $(a, c) ∈ R$, for every $a, b, c ∈ S$ None of the above.

Mk Utkarsh asked in Set Theory & Algebra May 12, 2018

1.1k views

3 votes

4 answers

175

ISRO2018-56
The time complexity of computing the transitive closure of binary relation on a set of $n$ elements is known to be $O(n)$ $O(n*\log(n))$ $O(n^{\frac{3}{2}})$ $O(n^{3})$

Arjun asked in Set Theory & Algebra Apr 22, 2018

by Arjun

2.1k views

0 votes

1 answer

176

Kenneth Rosen Edition 6th Exercise 6.1 Example 8 (Page No. 400)
Find a recurrence relation for Cn the number of ways to parenthesize the product of n+1 numbers , x0*x1*x2.......*xn , to specify the order of multiplication. For example C3 = 5 because there are five ways to parenthesize x0*x1*x2*.....*xn to determine the order of multiplication.

Abhinavg asked in Combinatory Mar 31, 2018

1.3k views

1 vote

1 answer

177

Set theory
Consider a set S $\left \{ 2,3,4,.....,23,24 \right \}$ and R is relation on S such that aRb if a divides b, then find the number of minimal elements in its hasse diagram

Mk Utkarsh asked in Set Theory & Algebra Mar 10, 2018

1.8k views

1 vote

1 answer

178

TEST SERIES
A binary relation R on Z × Z is deﬁned as follows: ( a , b ) R ( c , d ) iff a = c or b = d Consider the following propositions: 1. R is reflexive.2. R is symmetric. 3. R is antisymmetric. Which one of the following statements are True?

RahulRoy31 asked in Set Theory & Algebra Mar 2, 2018

530 views

1 vote

1 answer

179

Relation
For $a,b\epsilon Real$ define $aRb$ iff $a^{2}+b^{2}>2$.Is it Reflexive, Symmetric or Transitive?

srestha asked in Linear Algebra Jan 7, 2018

332 views

2 votes

1 answer

180

Relations
I'm getting 384....

Pawan Kumar 2 asked in Set Theory & Algebra Dec 31, 2017

by Pawan Kumar 2

296 views

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Recent questions tagged relations