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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
Irreflexive relation
If Irreflexive relation are represented as directed graphs, then the partitions of an equivalence relation manifest in the form of ______ A) Strongly connected component B) Unilaterally connected component C) Clique D) None of these
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Oct 6
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Set Theory & Algebra
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Lakshman Patel RJIT
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2
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?
asked
Oct 6
in
Set Theory & Algebra
by
sripo
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293
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relations
settheory&algebra
gate2019gate1987
0
votes
1
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3
Recurrence Relation
Let $T(n) = T(n1) + \frac{1}{n} , T(1) = 1 ;$ then $T(n) = ? $ $A) O(n^{2})$ $B) O(logn)$ $C) O(nlogn)$ $D) O(n^{2}logn)$
asked
Oct 5
in
Combinatory
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Lakshman Patel RJIT
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recurrenceeqation
0
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1
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4
Relation
State True or False? Empty set Φ is an equivalence relation.
asked
Sep 21
in
Set Theory & Algebra
by
srestha
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98.3k
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66
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relations
0
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1
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5
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.
asked
Aug 22
in
Set Theory & Algebra
by
superak96
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57
points)

24
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sets
relations
discretemathematics
0
votes
1
answer
6
State True/False
1. If f is bijective function then f1 is also bijective function. 2. If f is surjective function then f1 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.
asked
Aug 17
in
Set Theory & Algebra
by
Naveen Kumar 3
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22
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relations
functions
discretemathematics
+2
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2
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7
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 $R^m = R^n$.
asked
Aug 12
in
Set Theory & Algebra
by
Arjun
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359k
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79
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gate1998
descriptive
settheory&algebra
relations
0
votes
1
answer
8
Doubt
Is empty relation an equivalence relation?
asked
Aug 4
in
Set Theory & Algebra
by
aditi19
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849
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16
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relations
+2
votes
2
answers
9
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
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669
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45
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sql
databases
relations
0
votes
2
answers
10
UGCNETJuly2018II88
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)
asked
Jul 13
in
Others
by
Pooja Khatri
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4.3k
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35
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ugcnetjuly2018ii
discretemathematics
relations
+1
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0
answers
11
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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13.9k
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48
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kennethrosen
settheory&algebra
relations
algorithms
+1
vote
0
answers
12
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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13.9k
points)

42
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kennethrosen
settheory&algebra
relations
+1
vote
0
answers
13
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
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13.9k
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26
views
kennethrosen
settheory&algebra
relations
0
votes
0
answers
14
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
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(
13.9k
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28
views
kennethrosen
settheory&algebra
relations
0
votes
1
answer
15
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
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(
13.9k
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65
views
kennethrosen
settheory&algebra
relations
+1
vote
2
answers
16
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
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(
13.9k
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55
views
kennethrosen
settheory&algebra
relations
+1
vote
1
answer
17
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
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(
13.9k
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62
views
kennethrosen
settheory&algebra
relations
0
votes
0
answers
18
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
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(
13.9k
points)

31
views
kennethrosen
settheory&algebra
relations
0
votes
0
answers
19
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
(
13.9k
points)

40
views
kennethrosen
settheory&algebra
relations
0
votes
1
answer
20
Recurrence Relation
How to solve using recursion tree method T(n) = T(n/2) + c ; n > 1 T(n) = C ; n = 1
asked
Jun 10
in
Algorithms
by
Lakshman Patel RJIT
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9.6k
points)

148
views
algorithms
recurrence
relations
0
votes
1
answer
21
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
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(
13.3k
points)

35
views
settheory&algebra
discretemathematics
relations
0
votes
1
answer
22
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
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(
13.3k
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105
views
discretemathematics
settheory&algebra
relations
+1
vote
1
answer
23
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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57
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cmi2015
relations
settheory&algebra
+1
vote
2
answers
24
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
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9.6k
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251
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discretemathematics
settheory&algebra
equivalence
relations
+1
vote
1
answer
25
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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19.8k
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135
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discretemathematics
settheory&algebra
relations
0
votes
0
answers
26
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
(
181
points)

41
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discretemathematics
functions
relations
settheory&algebra
+4
votes
1
answer
27
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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74
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recurrence
relations
algorithms
+1
vote
0
answers
28
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
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98.3k
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47
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relations
+2
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1
answer
29
Relations
I'm getting 384....
asked
Dec 31, 2017
in
Set Theory & Algebra
by
Pawan Kumar 2
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4.6k
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91
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relations
0
votes
0
answers
30
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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8.2k
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103
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discretemathematics
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