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Use the google search bar on side panel. It searches through all previous GATE/other questions. For hardcopy of previous year questions please see
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Recent questions tagged relations
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1
GATE199810b
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 $R^m = R^n$.
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3 days
ago
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Set Theory & Algebra
by
Arjun
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355k
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28
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gate1998
descriptive
settheory&algebra
relations
0
votes
1
answer
2
Doubt
Is empty relation an equivalence relation?
asked
Aug 4
in
Set Theory & Algebra
by
aditi19
(
159
points)

12
views
relations
+1
vote
2
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3
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', ');
asked
Aug 1
in
Databases
by
Subham Nagar
Junior
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643
points)

17
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sql
databases
relations
0
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0
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4
RelationsKenneth Rosen(Ex 7.560)
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?
asked
Jun 30
in
Set Theory & Algebra
by
Ayush Upadhyaya
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10.9k
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43
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kennethrosen
settheory&algebra
relations
algorithms
0
votes
0
answers
5
RelationsKenneth Rosen(Ex 7.557)
Consider the equivalence relation R = $\{(x,y) \,  \, xy \,is\,an\,integer\}$ (b) What is the equivalence class of 1/2 for this equivalence relation?
asked
Jun 30
in
Set Theory & Algebra
by
Ayush Upadhyaya
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(
10.9k
points)

40
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kennethrosen
settheory&algebra
relations
0
votes
0
answers
6
RelationsKenneth Rosen(Ex 7.535)
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 when divided by 5. but in rosen answer is given in format $\{i\, \equiv 6mod5\}$ So is my answer same as given in text?
asked
Jun 30
in
Set Theory & Algebra
by
Ayush Upadhyaya
Boss
(
10.9k
points)

21
views
kennethrosen
settheory&algebra
relations
0
votes
0
answers
7
RelationsKenneth Rosen(Ex 7.42)
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 diagonal. After ... have to find the smallest relation containing R that is both symmetric and reflexive, then is the reflexive closure of R answer to this problem?
asked
Jun 30
in
Set Theory & Algebra
by
Ayush Upadhyaya
Boss
(
10.9k
points)

25
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kennethrosen
settheory&algebra
relations
0
votes
1
answer
8
RelationsKenneth Rosen(Ex 7.144)
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 "$a$" as their first element. (d) ... 1)}$ (e) $2^{(n1)^2}$ (f) $2^{n^2}2^{(n1)^2}$ Please let me know if my work is correct.
asked
Jun 29
in
Set Theory & Algebra
by
Ayush Upadhyaya
Boss
(
10.9k
points)

61
views
kennethrosen
settheory&algebra
relations
+1
vote
2
answers
9
RelationsKenneth Rosen(ex 7.135)
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)$R_4 o R_6$
asked
Jun 29
in
Set Theory & Algebra
by
Ayush Upadhyaya
Boss
(
10.9k
points)

53
views
kennethrosen
settheory&algebra
relations
+1
vote
1
answer
10
RelationsKenneth Rosen(Ex 7.148)
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?
asked
Jun 29
in
Set Theory & Algebra
by
Ayush Upadhyaya
Boss
(
10.9k
points)

58
views
kennethrosen
settheory&algebra
relations
0
votes
0
answers
11
RelationsKenneth Rosen (Ex 7.17)
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 satisfied. The various ... have RReflexive IRIrreflexive SSymmetric ATSAntisymmetric ASAsymmetric TTransitive. Let me know if below table entries are correct.
asked
Jun 29
in
Set Theory & Algebra
by
Ayush Upadhyaya
Boss
(
10.9k
points)

28
views
kennethrosen
settheory&algebra
relations
0
votes
0
answers
12
RelationsKenneth Rosen(Ex 7.16)
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 is satisfied. The ... have RReflexive IRIrreflexive SSymmetric ATSAntisymmetric ASAsymmetric TTransitive. Let me know if below table entries are correct.
asked
Jun 29
in
Set Theory & Algebra
by
Ayush Upadhyaya
Boss
(
10.9k
points)

34
views
kennethrosen
settheory&algebra
relations
0
votes
1
answer
13
Quasi Order Relations
What are the conditions for a relation to be quasiordered? 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 quasiorder if it is Reflexive and Transitive. Which one is correct ? or Am I missing something?
asked
Jun 6
in
Set Theory & Algebra
by
Soumya29
Boss
(
12k
points)

31
views
settheory&algebra
discretemathematics
relations
0
votes
1
answer
14
Problem in gate199810 part b 
Can someone help me in "part b" of this question https://gateoverflow.in/1724/gate199810 . 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 ?
asked
May 22
in
Set Theory & Algebra
by
Soumya29
Boss
(
12k
points)

99
views
discretemathematics
settheory&algebra
relations
+1
vote
1
answer
15
CMI2015A02
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 $(b, c) ∈ R$, for every $a, b ... b ∈ S$ If $R$ is Euclidean, $(a, b) ∈ R$ and $(b, c) ∈ R$, then $(a, c) ∈ R$, for every $a, b, c ∈ S$ None of the above.
asked
May 12
in
Set Theory & Algebra
by
Mk Utkarsh
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13.8k
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40
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cmi2015
relations
settheory&algebra
+1
vote
2
answers
16
Equivalence relation
Q)Which of the following is not an equivalence relation on a set of all real numbers? A) R1 = { (a,b) / ab is a integer } B) R2 = { (a,b) / ab is divisible by 5 } C) R3 = { (a,b) / ab is an odd number } D) R4 = { (a,b) / ab is an even number }
asked
Mar 11
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Loyal
(
8k
points)

245
views
discretemathematics
settheory&algebra
equivalence
relations
+1
vote
1
answer
17
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
asked
Mar 11
in
Set Theory & Algebra
by
Mk Utkarsh
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(
13.8k
points)

134
views
discretemathematics
settheory&algebra
relations
0
votes
0
answers
18
Composition of function
"f:A>B & g:C>D are 2 functions then for their composition B should be equal to C." But if B is not equal to C then composition is possible or not? Eg:A={1,2,} B={3,4} C={4,5} D={6,7} then can fog be computed Or not? f={(1,3), (2,4)} g={(4,6),(5,7)} gof={(2,6)} is it true or not? I hope my question could be understood:)
asked
Mar 3
in
Combinatory
by
MayankSharma
(
153
points)

37
views
discretemathematics
functions
relations
settheory&algebra
+4
votes
1
answer
19
recurence relation
Which of the following represents most appropriate asymptotic solution for given reccurance: (A) O(n) (B) O(log n) (C) O(log log n) (D) O(log n)2
asked
Jan 15
in
Algorithms
by
Lakshman Patel RJIT
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(
8k
points)

71
views
recurrence
relations
algorithms
+1
vote
0
answers
20
Relation
For $a,b\epsilon Real$ define $aRb$ iff $a^{2}+b^{2}>2$.Is it Reflexive, Symmetric or Transitive?
asked
Jan 7
in
Linear Algebra
by
srestha
Veteran
(
91.6k
points)

46
views
relations
+2
votes
1
answer
21
Relations
I'm getting 384....
asked
Dec 31, 2017
in
Set Theory & Algebra
by
Pawan Kumar 2
Active
(
4.5k
points)

89
views
relations
0
votes
0
answers
22
Relation Reflexive Irreflexive
$Let A = \{ 1,2,3\}\\ R = \{\{1,1\},\{2,2\},\{2,3\}\}$ Is the above relation neither reflexive nor irreflexive?
asked
Dec 28, 2017
in
Set Theory & Algebra
by
Tuhin Dutta
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(
7.9k
points)

96
views
discretemathematics
settheory&algebra
relations
+2
votes
0
answers
23
relation
asked
Dec 27, 2017
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Loyal
(
8k
points)

16.1k
views
relations
0
votes
1
answer
24
Question on Relations
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 is True?
asked
Dec 22, 2017
in
Set Theory & Algebra
by
Durgesh Singh
Junior
(
877
points)

147
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settheory&algebra
relations
discretemathematics
+1
vote
2
answers
25
DBMS : Referential integrity constraints
asked
Dec 17, 2017
in
Databases
by
rahul sharma 5
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24.4k
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210
views
databases
referentialintegrity
relations
+4
votes
1
answer
26
ISRODEC20172
Consider the set of integers $I.$ Let $D$ denote "divides with an integer quotient" (e.g. $4D8$ but not $4D7$). Then $D$ is Reflexive, Not Symmetric, Transitive Not Reflexive, Not Antisymmetric, Transitive Reflexive, Antisymmetric, Transitive Not Reflexive, Not Antisymmetric, Not Transitive
asked
Dec 17, 2017
in
Set Theory & Algebra
by
gatecse
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isrodec2017
settheory&algebra
relations
0
votes
1
answer
27
No. of tables for ER diagram
How many minimum tables are required for this er diagram consisting of a many  many relation and total participation of one of the entities.? Can't i merge relation R and entity B? why?
asked
Dec 5, 2017
in
Databases
by
aditya kuppa 1
(
113
points)

206
views
gatebook_dbms
databases
ertorelational
relations
+1
vote
1
answer
28
Relational algebra
Consider the relations r1(P, Q, R) and r2(R, S, T) with primary keys P and R respectively. The relation r1 contains 2000 tuples and r2 contains 2500 tuples. The maximum size of the join r1⋈ r2 is equal to r2⋈ r1 true or false?
asked
Dec 3, 2017
in
Databases
by
learner_geek
Active
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3.5k
points)

177
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relationalcalculus
joins
relations
relationalalgebra
databases
+2
votes
2
answers
29
relational algebra
Consider the following schema: Student (Sid, Sname, age) Course Info (Cid, Cname, Instructor SSN) Enroll (Sid, Cid, grade). The relational algebra expression for “find the Cid’s of courses enrolled by two different students” (no options)
asked
Dec 3, 2017
in
Databases
by
shaurya vardhan
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(
2.2k
points)

161
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databases
relationalalgebra
relations
relationalcalculus
+2
votes
2
answers
30
#dbms relational algebra
Consider the following relations A, B and C: A Id Name Age 12 Arun 60 15 Shreya 24 99 Rohit 11 B Id Name Age 15 Shreya 24 25 Hari 40 98 Rohit 20 99 Rohit 11 C Id Phone Area 10 2200 02 99 2100 01 How many tuples does the result of the following relational algebra expression contain? Assume that the schema of A∪B is the same as that of A. (A∪B)⋈A.Id>40∧C.Id<15C
asked
Dec 2, 2017
in
Databases
by
iarnav
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7.9k
points)

103
views
databases
relationalalgebra
relations
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