GATE Overflow - Recent questions tagged relations
https://gateoverflow.in/tag/relations
Powered by Question2AnswerDifference between Anti and Asymmetric?
https://gateoverflow.in/171560/difference-between-anti-and-asymmetric
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=14136978048900584255"></p>Set Theory & Algebrahttps://gateoverflow.in/171560/difference-between-anti-and-asymmetricSat, 18 Nov 2017 10:03:19 +0000Equivalence Relation
https://gateoverflow.in/170535/equivalence-relation
<p><img alt="" height="161" src="https://gateoverflow.in/?qa=blob&qa_blobid=15267125372007620724" width="778"></p>
<p>Which of the above are true.</p>
<p>I think only 1st one is true. But the answer given is all are true.</p>Set Theory & Algebrahttps://gateoverflow.in/170535/equivalence-relationWed, 15 Nov 2017 14:14:26 +0000projection in relational algebra
https://gateoverflow.in/168911/projection-in-relational-algebra
<p>For the relation instances A and B, A/B is the largest relation instance Q such that Q × B ⊆ A. Consider A has exactly two fields x and y and B has just one field y with the same domain as in A. Division operation A/B is defined as the set of all x values (in the form of unary tuples) such that for every y value in (a tuple of) B, there is a tuple (x, y) in A. A/B can be defined using the algebra expression.</p>
<p>(A) π<sub>x</sub>(A) - π<sub>x</sub>((π<sub>x</sub>(A) × B) - B)
<br>
(B) π<sub>x</sub>(A) - π<sub>x</sub>((π<sub>x</sub>(B) × A) - B)
<br>
(C) π<sub>x</sub>(A) - π<sub>x</sub>((π<sub>x</sub>(A) × B) - A)
<br>
(D) π<sub>x</sub>(A) - π<sub>x</sub>((π<sub>x</sub>(B) × A) - A)</p>Databaseshttps://gateoverflow.in/168911/projection-in-relational-algebraSat, 11 Nov 2017 16:53:58 +0000ace test series
https://gateoverflow.in/164726/ace-test-series
<p>If $A=\left \{ 1,2,3 \right \}$, then number of relations possible on $A$, which are neither reflexive nor symmetric is _____________ </p>
<p><img alt="" height="127" src="https://gateoverflow.in/?qa=blob&qa_blobid=2140432965675930287" width="747"></p>Set Theory & Algebrahttps://gateoverflow.in/164726/ace-test-seriesWed, 01 Nov 2017 09:03:33 +0000Discrete Maths :- Relations
https://gateoverflow.in/163654/discrete-maths-relations
Check if the following relation is Antisymmetric,where R is defined on set of integers<br />
<br />
R ={ (x,y) | y=$x^i$, for some i $\varepsilon$ Z}Set Theory & Algebrahttps://gateoverflow.in/163654/discrete-maths-relationsSat, 28 Oct 2017 20:02:36 +0000Rossen: How to perform Composition on Directed Graph.
https://gateoverflow.in/159587/rossen-how-to-perform-composition-on-directed-graph
<p>Given the directed graphs representing two relations, how can the directed graph of the union, intersection, symmetric difference, difference, and composition of these relations be found?</p>
<p>As, we can easily find, union, intersection, difference and symmetric difference. But how we can find composition of directed graph.</p>
<p>There is a ref:- <a rel="nofollow" href="https://math.stackexchange.com/questions/239897/draw-the-composition-of-directed-graphs">https://math.stackexchange.com/questions/239897/draw-the-composition-of-directed-graphs</a></p>
<p>But not explained clearly.</p>Set Theory & Algebrahttps://gateoverflow.in/159587/rossen-how-to-perform-composition-on-directed-graphFri, 13 Oct 2017 03:15:23 +0000kenneth rosen relations
https://gateoverflow.in/158028/kenneth-rosen-relations
How many of the 16 different relations on {0,1} contain the pair (0,1)?Combinatoryhttps://gateoverflow.in/158028/kenneth-rosen-relationsSat, 07 Oct 2017 07:01:40 +0000Relations
https://gateoverflow.in/157250/relations
<p>Consider the set <em>S</em> = {<em>a</em>, <em>b</em>} and ‘<em>L</em>’ be a binary relation such that <em>L</em> = {all binary relations except reflexive relation set <em>S</em>}. The number of relation which are symmetric _______.</p>Set Theory & Algebrahttps://gateoverflow.in/157250/relationsWed, 04 Oct 2017 16:25:16 +0000Equivalence and Inverse of Relation.
https://gateoverflow.in/149325/equivalence-and-inverse-of-relation
Proof the following statement.<br />
<br />
1. If R1 and R2 are the equivalence relation on X then R1 $\cap$ $R2^{-1}$ (Inverse of R2) is also an equivalence relation.<br />
<br />
2. If R is reflexive and transitive relation on X then R $\cap$ $R^{-1}$ is an equivalence relation.Set Theory & Algebrahttps://gateoverflow.in/149325/equivalence-and-inverse-of-relationSat, 02 Sep 2017 15:36:34 +0000relations
https://gateoverflow.in/147198/relations
what is the Number of relations S over set {0,1,2,3} such that (x,y) belongs to S=> x=ySet Theory & Algebrahttps://gateoverflow.in/147198/relationsFri, 25 Aug 2017 18:18:50 +0000Relations
https://gateoverflow.in/142068/relations
Consider the set {2,3,4} and define partial ordering if a divides b.<br />
<br />
Now element 3 is maximal or minimal.Set Theory & Algebrahttps://gateoverflow.in/142068/relationsSun, 06 Aug 2017 11:28:44 +0000Relations: Doubt About Composites (Conceptual)
https://gateoverflow.in/139396/relations-doubt-about-composites-conceptual
<p>If R is any relation:</p>
<p>is R<sup>n</sup>o R (composite of R<sup>n </sup>and R) the same as R o R<sup>n</sup>?</p>
<p> </p>Set Theory & Algebrahttps://gateoverflow.in/139396/relations-doubt-about-composites-conceptualSun, 23 Jul 2017 12:11:19 +0000Recurrence relations
https://gateoverflow.in/138106/recurrence-relations
<div style="background:#eeeeee;border:1px solid #cccccc;padding:5px 10px;">T(n)=T(n/2+2)+n</div>
<div style="background:#eeeeee;border:1px solid #cccccc;padding:5px 10px;">Solution using substitution method</div>Algorithmshttps://gateoverflow.in/138106/recurrence-relationsSun, 16 Jul 2017 05:28:35 +0000DBMS Relational Algebra
https://gateoverflow.in/137637/dbms-relational-algebra
<p>How the following two expressions are equal?</p>
<p> </p>
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=8526610146442016788"></p>
<p>The LHS will remove duplicates but RHS will not.Please explain</p>Databaseshttps://gateoverflow.in/137637/dbms-relational-algebraThu, 13 Jul 2017 15:41:57 +0000Relation and Partial order
https://gateoverflow.in/136517/relation-and-partial-order
<p> </p>
<p>Is (<em>S, R</em>) a <strong>poset </strong>if <em>S </em>is the set of all people in the world and (<em>a, b</em>) <em>∈ </em><em>R</em>, where <em>a </em>and <em>b </em>are people,
<br>
if <strong><em>a </em>is not taller than <em>b</em></strong>?
<br>
</p>Set Theory & Algebrahttps://gateoverflow.in/136517/relation-and-partial-orderFri, 07 Jul 2017 11:35:52 +0000Problem related to Equivalence relation
https://gateoverflow.in/136171/problem-related-to-equivalence-relation
<h3><strong>R </strong>is a relation on the set of all <strong>functions </strong>from <strong>Z </strong>to <strong>Z</strong>.</h3>
<h3><strong>R = { (f, g) | for some C ∈ Z , for all x ∈ Z , f(x) - g(x) = C } </strong></h3>
<p>is it <strong>Equivalence relation </strong>or not ?</p>Set Theory & Algebrahttps://gateoverflow.in/136171/problem-related-to-equivalence-relationWed, 05 Jul 2017 13:13:30 +0000Relations
https://gateoverflow.in/136095/relations
Please tell me how to calculate total number of symmetric relations on a set of 5 elements.<br />
<br />
I know the answer but want the proof.Set Theory & Algebrahttps://gateoverflow.in/136095/relationsWed, 05 Jul 2017 04:47:43 +0000Problem related to irreflexive (Relation)
https://gateoverflow.in/134951/problem-related-to-irreflexive-relation
<h2>Given Relation is <strong>irreflexive</strong> or not ?</h2>
<h1>R = { (a,b) | <strong>there is at least one common link on Web page <span class="marker"><em>a </em></span>and Web page <span class="marker"><em>b</em></span></strong><span class="marker"> </span>}</h1>Set Theory & Algebrahttps://gateoverflow.in/134951/problem-related-to-irreflexive-relationTue, 27 Jun 2017 12:56:38 +0000Discrete maths equivalence relation
https://gateoverflow.in/132834/discrete-maths-equivalence-relation
Consider the equivalence relation<br />
namely, R = (x, y) I x - y is an integer}.<br />
<br />
What is the equivalence class of R={ (x,y) | x-y in integer(Z)} equivalence<br />
relation?<br />
<br />
Given answer is :- (n + 1/2 I n E Z)<br />
<br />
My answer is :- (n*1/2 | n E Z)<br />
<br />
<br />
<br />
Is my answer correct also?Mathematical Logichttps://gateoverflow.in/132834/discrete-maths-equivalence-relationMon, 12 Jun 2017 20:41:16 +0000Views and Tables
https://gateoverflow.in/131676/views-and-tables
What is the difference between a View and a Table?<br />
<br />
If I create a Table, it will be stored in the database. I mean on the storage space.<br />
<br />
If I create a View, it will not be stored onto the storage space?<br />
<br />
Please correct me if I am wrong?Databaseshttps://gateoverflow.in/131676/views-and-tablesSat, 03 Jun 2017 02:09:21 +0000Kenneth Rosen Edition7 Ch-7 Ex-1 QueNo-5
https://gateoverflow.in/131099/kenneth-rosen-edition7-ch-7-ex-1-queno-5
<p>Determine whether the relation R on the set of all Web
<br>
pages is reflexive, Irreflexive, symmetric, antisymmetric, and/or transitive,
<br>
where (a, b) ∈ R if and only if
<br>
a) everyone who has visitedWeb page a has also visited
<br>
Web page b.
<br>
b) there are no common links found on both Web
<br>
page a andWeb page b.
<br>
c) there is at least one common link onWeb page a and
<br>
Web page b.
<br>
d) there is a Web page that includes links to both Web
<br>
page a andWeb page b.
<br>
<br>
<strong>Why option a is not symmetric but reflexive? why option c and d is not reflexive?</strong>
<br>
Please explain it with clear example. Thank you.</p>Set Theory & Algebrahttps://gateoverflow.in/131099/kenneth-rosen-edition7-ch-7-ex-1-queno-5Sat, 27 May 2017 15:59:34 +0000ISRO2017-80
https://gateoverflow.in/128781/isro2017-80
The time complexity of computing the transitive closure of a binary relation on a set of $n$ elements is known to be<br />
<br />
a. $O(n\log n)$<br />
<br />
b. $O\left( n^{3/2}\right)$<br />
<br />
c. $O( n^3 )$<br />
<br />
d. $O(n)$Algorithmshttps://gateoverflow.in/128781/isro2017-80Sun, 07 May 2017 22:43:11 +0000tables in Self Referential relations
https://gateoverflow.in/127908/tables-in-self-referential-relations
<p>Plz explain what is the no of tables required in self referential relation( without multivalued attribute) and How:-</p>
<p> <img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=5376542220233314230"></p>
<p>and also (with multivalued attribute) ?</p>
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=16979386322095582645"></p>
<p>???</p>Databaseshttps://gateoverflow.in/127908/tables-in-self-referential-relationsWed, 03 May 2017 10:16:05 +0000Relations
https://gateoverflow.in/121896/relations
Proof that a relation which is symmetric and transitive, need not be reflexive relation.Mathematical Logichttps://gateoverflow.in/121896/relationsFri, 17 Mar 2017 12:05:33 +0000Relations
https://gateoverflow.in/119358/relations
Let A={1,2,3,4,5,6,7}<br />
What will be no of symmetric relations on A that contains exactly 4 ordered pairs?Set Theory & Algebrahttps://gateoverflow.in/119358/relationsSun, 19 Feb 2017 14:07:44 +0000The Relation is ?
https://gateoverflow.in/111254/the-relation-is
<p><em>Suppose there is a set L ,set of lines and there is a Relation R,</em></p>
<p><strong>R={<L1,L2> ϵ R if L1 || L2 | L1,L2 ϵ L }.</strong></p>
<p><strong>Relation R is, _______________.</strong></p>
<p><strong>1. Reflexive</strong></p>
<p><strong>2.Symmetric</strong></p>
<p><strong>3.Antisymmetric</strong></p>
<p><strong>4.Asymmetric</strong></p>
<p><strong>5.Transitive.</strong></p>
<p><strong>Explanation in simple words with Example will be appreciated.</strong></p>
<p><strong>Thanks.</strong></p>Set Theory & Algebrahttps://gateoverflow.in/111254/the-relation-isWed, 25 Jan 2017 23:36:36 +0000type of relation
https://gateoverflow.in/109601/type-of-relation
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=13405252837237460237"></p>
<p>how is it not transitive??</p>
<p>i mean take any time instant.ie x= 4:00 and y=4:20,z= 4:40..they are transitive..right??</p>Set Theory & Algebrahttps://gateoverflow.in/109601/type-of-relationMon, 23 Jan 2017 14:02:05 +0000Geeks for Geeks
https://gateoverflow.in/105062/geeks-for-geeks
<p>A and B are two sets. If |A| = 5 , |B| = 3 , then, the number of onto functions from A to B are ___ ?</p>
<p><strong>(A)</strong> 35
<br>
<strong>(B)</strong> 150
<br>
<strong>(C)</strong> 29
<br>
<strong>(D)</strong> 27</p>Mathematical Logichttps://gateoverflow.in/105062/geeks-for-geeksFri, 13 Jan 2017 17:45:13 +0000Relations and Combinatorics
https://gateoverflow.in/101502/relations-and-combinatorics
$\begin{align*} &S = \left \{ G_i \;\; | \; G_i \in \text{ lebeled trees with 4 vertices} \right \} \\ &\text{Relation } \quad R = \left \{ {\color{red}{\left ( G_i,G_j \right )}} \; | G_i,G_j \in S \;\; \text{and} \;\; G_i,G_j \;\; \text{are} \;\; \text{isomorphic to each other} \right \} \end{align*}$<br />
<br />
No of equivalent classes of $R$ ?Combinatoryhttps://gateoverflow.in/101502/relations-and-combinatoricsFri, 06 Jan 2017 16:17:34 +0000Maths: Counting Relations
https://gateoverflow.in/99470/maths-counting-relations
<p>Let A = {1,2,3,4}. since each element of P(AxA) is subset of AxA, it is binary relation on A
<br>
Assuming each relation in P(AxA) is equally likely to be chosen,
<br>
<br>
i. what is the probability that a randomly chosen relation is reflexive
<br>
a. 1/2<sup>6</sup>
<br>
b. 1/2<sup>4</sup>
<br>
c. 1/2<sup>6</sup>
<br>
d. 1/2<sup>12</sup>
<br>
<span class="marker">Given Ans: 1/2<sup>4</sup></span>
<br>
ii what is the probability that a randomly chosen relation is Symmetric
<br>
a. 1/2<sup>16</sup>
<br>
b. 1/2<sup>4</sup>
<br>
c. 1/2<sup>6</sup>
<br>
d. 1/2<sup>12</sup>
<br>
<span class="marker">Given Ans: 1/2<sup>6</sup></span></p>Set Theory & Algebrahttps://gateoverflow.in/99470/maths-counting-relationsMon, 02 Jan 2017 15:24:13 +0000Maths: Relations
https://gateoverflow.in/99345/maths-relations
<p>An Equivalence relation R on Z defined by <sub>a</sub>R<sub>b </sub>if 5a=2b(mod3). which of the following is an equivalence class of R?
<br>
1. The Set {x ∈ Z: x=3y for some y∈Z}
<br>
2. The even integers
<br>
3. The odd integers
<br>
4. the set {x<sup>2 </sup>: x ∈ Z}</p>Set Theory & Algebrahttps://gateoverflow.in/99345/maths-relationsMon, 02 Jan 2017 11:00:07 +0000Relation
https://gateoverflow.in/92673/relation
<p>Which of the following is/are true ?</p>
<ul>
<li>A. $\text{R}$ is a reflexive relation on a set $\text{A}$, then $\text{R}^{n}$ is reflexive for all $n\geq0$</li>
<li>B. Relation $\text{R}$ on set $A$ is reflexive if and only if inverse relation $R^{-1}$ is reflexive.</li>
<li>C Relation $\text{R}$ on set $A$ is antisymmetric if and only $R \cap R^{-1}$ is a subest of diagonal relation $\Delta = \left \{ (a,a) \; | a \in A \right \}$</li>
<li>D. $M_{S\circ R} = M_R \; \odot M_S$ where $\odot$ is boolean product.</li>
</ul>Set Theory & Algebrahttps://gateoverflow.in/92673/relationWed, 14 Dec 2016 18:30:03 +0000Relation composition
https://gateoverflow.in/92672/relation-composition
$R$ and $S$ are two relations on a set $A$<br />
<br />
$$\begin{align*} M_R = \begin{bmatrix} 1 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ \end{bmatrix} \qquad M_S = \begin{bmatrix} 0 & 1 & 1 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \\ \end{bmatrix} \end{align*}$$<br />
<br />
Then matrices for $R \cap S$ and $R \cup S$ ?Set Theory & Algebrahttps://gateoverflow.in/92672/relation-compositionWed, 14 Dec 2016 18:30:00 +0000Relation
https://gateoverflow.in/92671/relation
<p>How many non zero entries does the matrix representing relation $R$ on a set $A$ = $\left \{ 1,2,3,4,5,6....1000 \right \}$.</p>
<ul>
<li>a. $R = \left \{ (x,y) \; | x = y \pm 1 \right \}$</li>
<li>b. $R = \left \{ (x,y) \; | x + y = 1000 \right \}$</li>
</ul>Set Theory & Algebrahttps://gateoverflow.in/92671/relationWed, 14 Dec 2016 18:29:52 +0000Equivalence relation
https://gateoverflow.in/92670/equivalence-relation
<p>True / false ?</p>
<ul>
<li>a. Partitions formed from congruence classes modulo $6$ is a refinement of the partitions formed from congruence classes modulo 3</li>
<li>s and t are bit strings and $R_n = \left \{ (s,t) \; | s = t \; \text{or} \; \text{ s and t are bit strings with at least n characters that agree on their first n characters} \right \}$
<ul>
<li>then $R_4$ creates refinement partitions with respect to the partitions of $R_3$. </li>
</ul>
</li>
</ul>Set Theory & Algebrahttps://gateoverflow.in/92670/equivalence-relationWed, 14 Dec 2016 18:29:40 +0000equivalence relaton
https://gateoverflow.in/90931/equivalence-relaton
<p>How many different equivalence relations with exactly three equivalence classes are there on a set with 5 elements</p>
<ol>
<li>10</li>
<li>15</li>
<li>25</li>
<li>30</li>
</ol>
<p> </p>Set Theory & Algebrahttps://gateoverflow.in/90931/equivalence-relatonFri, 09 Dec 2016 09:33:23 +0000Gateforum DBMS assesment test(Relational Algebra)(see the image below)
https://gateoverflow.in/90084/gateforum-dbms-assesment-test-relational-algebra-image-below
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=14267363148558989904"></p>Databaseshttps://gateoverflow.in/90084/gateforum-dbms-assesment-test-relational-algebra-image-belowTue, 06 Dec 2016 16:56:32 +0000GateForum DBMS Assessment test(see the image below)
https://gateoverflow.in/89118/gateforum-dbms-assessment-test-see-the-image-below
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=11984714130027318968"></p>Databaseshttps://gateoverflow.in/89118/gateforum-dbms-assessment-test-see-the-image-belowSat, 03 Dec 2016 19:20:34 +0000GATE1989-1-iv
https://gateoverflow.in/87048/gate1989-1-iv
The transitive closure of the relation $\left\{(1, 2), (2, 3), (3, 4), (5, 4)\right\}$ on the set $\left\{1, 2, 3, 4, 5\right\}$ is ___________.Set Theory & Algebrahttps://gateoverflow.in/87048/gate1989-1-ivSun, 27 Nov 2016 16:19:28 +0000GATE1987-9e
https://gateoverflow.in/82446/gate1987-9e
How many true inclusion relations are there of the from $A \subseteq B$, where $A$ and $B$ are subsets of a set $S$ with $n$ elements?Set Theory & Algebrahttps://gateoverflow.in/82446/gate1987-9eTue, 15 Nov 2016 00:52:56 +0000GATE1987-9a
https://gateoverflow.in/82436/gate1987-9a
How many binary relations are there on a set $A$ with $n$ elements?Set Theory & Algebrahttps://gateoverflow.in/82436/gate1987-9aTue, 15 Nov 2016 00:37:08 +0000GATE1987-2d
https://gateoverflow.in/80583/gate1987-2d
State whether the following statements are TRUE or FALSE:<br />
<br />
The union of two equivalence relations is also an equivalence relation.Set Theory & Algebrahttps://gateoverflow.in/80583/gate1987-2dWed, 09 Nov 2016 18:40:45 +0000set theory
https://gateoverflow.in/78138/set-theory
What is the number of relations which are either symmetric or antisymmetric on a set with 3 elements?Set Theory & Algebrahttps://gateoverflow.in/78138/set-theoryWed, 02 Nov 2016 05:59:21 +0000Doubt
https://gateoverflow.in/74779/doubt
A $\phi$ (empty) relation on any set $A$ is not reflexive because for every $ a \in A$, $(a, a) \notin \phi$, but $\phi$ is a symmetric as well as transitive relation on $A$, how is that possible $?$Set Theory & Algebrahttps://gateoverflow.in/74779/doubtMon, 17 Oct 2016 20:46:18 +0000UGCNET-June2010-II-1
https://gateoverflow.in/67601/ugcnet-june2010-ii-1
<p>"$x^{1}$ is a clone of $x$" means $x^{1}$ is identical to $x$ in terms of the physical attributes namely, height, weight and complexion. Given, height, weight and complexion only form a complete set of attributes for an entity, cloning is an equivalence relation. What is your impression about this statement ?</p>
<ol style="list-style-type:upper-alpha">
<li>The statement is true</li>
<li>The statement is false</li>
<li>The truth value of the statement cannot be computed</li>
<li>None of these</li>
</ol>Set Theory & Algebrahttps://gateoverflow.in/67601/ugcnet-june2010-ii-1Wed, 14 Sep 2016 00:19:58 +0000RELATIONS
https://gateoverflow.in/62447/relations
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). What are the equivalence classes of R?Set Theory & Algebrahttps://gateoverflow.in/62447/relationsTue, 09 Aug 2016 07:25:18 +0000