GATE Overflow - Recent questions in Set Theory & Algebra
https://gateoverflow.in/questions/mathematics/discrete-mathematics/set-theory-%26-algebra
Powered by Question2AnswerRossen: 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 +0000he number of students who take both the subjects mathematics and chemistry is 30
https://gateoverflow.in/158530/number-students-take-subjects%C2%A0mathematics%C2%A0and-chemistry
The number of students who take both the subjects mathematics and chemistry is 30. This represents 10% of the enrolment in mathematics and 12% of the enrollment in Chemistry. How many students take atleast one of these two subjects?Set Theory & Algebrahttps://gateoverflow.in/158530/number-students-take-subjects%C2%A0mathematics%C2%A0and-chemistryMon, 09 Oct 2017 06:33:27 +0000Inverse of a function
https://gateoverflow.in/158002/inverse-of-a-function
Consider a function f from A to B such that f : A → B is bijective.<br />
f–1 represents inverse of f.<br />
Than could we say that f-1 :B->A is also bijective..Please give proper reasoning thanksSet Theory & Algebrahttps://gateoverflow.in/158002/inverse-of-a-functionSat, 07 Oct 2017 05:50:01 +0000Discrete-mathematics
https://gateoverflow.in/157333/discrete-mathematics
Consider the following statements <br />
<br />
1) If f is one-to-one function from an infinite set A to itself then f must be onto.<br />
<br />
2) If f is one-to-one function from an finite set A to itself then f must be onto.<br />
<br />
3) Power set of countably infinite set is countably infinite.<br />
<br />
which of the following is true - <br />
<br />
1) I only<br />
<br />
2) I and II only<br />
<br />
3) All are true.<br />
<br />
4) II onlySet Theory & Algebrahttps://gateoverflow.in/157333/discrete-mathematicsThu, 05 Oct 2017 01:24:20 +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 +0000Set theory
https://gateoverflow.in/157200/set-theory
<div>
<p>The number of pairs of set (<em>X</em>, <em>Y</em>) are there that satisfy the condition <em>X</em>, <em>Y</em> ⊆ {1, 2, 3, 4, 5, 6} and <em>X</em> ∩ <em>Y</em> = Φ ________.</p>
</div>
<div>
<ul>
</ul>
</div>Set Theory & Algebrahttps://gateoverflow.in/157200/set-theoryWed, 04 Oct 2017 12:24:38 +0000Set Theory and algebra
https://gateoverflow.in/157194/set-theory-and-algebra
<p>If we are given a set for ex.S={1,2,.....25} and now if we want to find subsets T ⊆ S of size 5 than it is 25C<sub>5</sub> or they are 2^ 25C<sub>5.</sub></p>Set Theory & Algebrahttps://gateoverflow.in/157194/set-theory-and-algebraWed, 04 Oct 2017 11:52:55 +0000set theory and algebra
https://gateoverflow.in/157037/set-theory-and-algebra
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=7506087194220041859"></p>Set Theory & Algebrahttps://gateoverflow.in/157037/set-theory-and-algebraTue, 03 Oct 2017 17:09:38 +0000relation doubt
https://gateoverflow.in/157010/relation-doubt
Number of relation S over set (0,1,2,3) such that (x,y) E S --> x =ySet Theory & Algebrahttps://gateoverflow.in/157010/relation-doubtTue, 03 Oct 2017 16:03:12 +0000#GroupTheory #TestBook
https://gateoverflow.in/156768/%23grouptheory-%23testbook
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=5980799671753357046"></p>Set Theory & Algebrahttps://gateoverflow.in/156768/%23grouptheory-%23testbookMon, 02 Oct 2017 15:13:25 +0000#GroupTheory #TestBook
https://gateoverflow.in/156767/%23grouptheory-%23testbook
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=6723155370129365533"></p>
<p>Plz explain this question</p>Set Theory & Algebrahttps://gateoverflow.in/156767/%23grouptheory-%23testbookMon, 02 Oct 2017 15:08:12 +0000Group Theory
https://gateoverflow.in/156722/group-theory
<p>Let (G,<em>star) be a group such that for any a,b belongs to G, (a</em>b)power^71==(a)power^71 * (b)power^71, (ab)power^72==(a)power^72 * (b)power^72 and (ab)power^73=(a)power^73 * (b)power^73. Proove that G is Abelian Group.</p>Set Theory & Algebrahttps://gateoverflow.in/156722/group-theoryMon, 02 Oct 2017 10:56:28 +0000ace test
https://gateoverflow.in/156332/ace-test
How mny relations they satisfy the property of equivalence relation as well as partial order over set A={1,2,3,4}.Set Theory & Algebrahttps://gateoverflow.in/156332/ace-testSat, 30 Sep 2017 10:59:48 +0000UGCNET-june2006-5
https://gateoverflow.in/156107/ugcnet-june2006-5
<div style="margin-left:25.2pt;">Let A = {x | -1<x<1} = B. The function f(x)=x/2 from A to B is:</div>
<div style="margin-left:25.2pt;">(A) injective </div>
<div style="margin-left:25.2pt;">(B) surjective</div>
<div style="margin-left:25.2pt;">(C) both injective and surjective</div>
<div style="margin-left:25.2pt;">(D) neither injective nor surjective</div>
<p> </p>Set Theory & Algebrahttps://gateoverflow.in/156107/ugcnet-june2006-5Fri, 29 Sep 2017 12:00:38 +0000UGCNET-dec2008-ii-12
https://gateoverflow.in/155035/ugcnet-dec2008-ii-12
<p><strong>A relation R in {1,2,3,4,5,6} is given by {(1,2),(2,3),(3,4),(4,4),(4,5)}. This relation is:</strong></p>
<p><strong>(A) reflexive </strong></p>
<p><strong>(B) symmetric</strong></p>
<p><strong>(C) transitive </strong></p>
<p><strong>(D) not reflexive, not symmetric and not transitive</strong></p>Set Theory & Algebrahttps://gateoverflow.in/155035/ugcnet-dec2008-ii-12Mon, 25 Sep 2017 09:47:37 +0000graph theory
https://gateoverflow.in/153771/graph-theory
<p><strong>"A planar graph need not to be connected" </strong></p>
<p>Can someone plz explain with an example .</p>Set Theory & Algebrahttps://gateoverflow.in/153771/graph-theoryWed, 20 Sep 2017 18:33:56 +0000Problem in sets
https://gateoverflow.in/153321/problem-in-sets
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=7932127215028874940"></p>
<p>more than 1 can be true or false </p>Set Theory & Algebrahttps://gateoverflow.in/153321/problem-in-setsTue, 19 Sep 2017 04:05:22 +0000Maths: functions: is given function bijective?
https://gateoverflow.in/153316/maths-functions-is-given-function-bijective
<p><strong>Question</strong> Determine whether the following function from R to R is a bijection
<br>
f(x) = $\frac{(x+1)}{(x+2)}$</p>
<p><strong>Solution:</strong>
<br>
First of all, this is not a function because f(-2) is not defined.</p>
<p>So, if the domain of the function is R - {-2} then this function is one-to-one.</p>
<p>And, if co-domain of this function is R - {1} then this function is onto.</p>
<p>So, the given function is bijection but with two above mentioned conditions. can someone please confirm?</p>
<p> </p>Set Theory & Algebrahttps://gateoverflow.in/153316/maths-functions-is-given-function-bijectiveTue, 19 Sep 2017 03:42:18 +0000Self doubt - Power Set
https://gateoverflow.in/153076/self-doubt-power-set
<p>Can you conclude A = B if A and B are 2 sets with the same power set ?
<br>
<br>
<strong>Doubt : Is power set of a set unique ?</strong></p>Set Theory & Algebrahttps://gateoverflow.in/153076/self-doubt-power-setMon, 18 Sep 2017 06:02:52 +0000Function Composition
https://gateoverflow.in/153066/function-composition
<blockquote>
<p><em><strong>For gof to be one-to-one, f must be one-to-one but reverse is not true.</strong></em></p>
</blockquote>
<p>Is the above statement correct?</p>
<p><strong>According to me both f and g must be one-to-one for gof to be one-to-one.</strong></p>
<p>I took below examples:</p>
<p>(i) f is one-to-one and g is onto</p>
<p>Let A = {1, 2, 3}, B = {a, b, c} and C = {α, β}.</p>
<p>Given f: A -> B where f(1) = a, f(2) = b, f(3) = c and g: B -> C where g(a) = α, g(b) = α, g(c) = β.</p>
<p>Then, gof: A -> C which gives g(f(1)) = g(a) = α, g(f(2)) = g(b) = α and g(f(3)) = g(c) = β.</p>
<p>Here, g(f(1)) and g(f(2)) both gives α which implies that <strong>gof is not one-to-one</strong>.</p>
<p> </p>
<p>(ii) f is onto and g is one-to-one</p>
<p>Let A = {1, 2, 3}, B = {a, b} and C = {α, β}.</p>
<p>Given f: A -> B where f(1) = a, f(2) = a, f(3) = b and g: B -> C where g(a) = α, g(b) = α.</p>
<p>Then, gof: A -> C which gives g(f(1)) = g(a) = α, g(f(2)) = g(a) = α and g(f(3)) = g(b) = β.</p>
<p>Here, also g(f(1)) and g(f(2)) both gives α which implies that <strong>gof is not one-to-one</strong>.</p>
<p> </p>
<p>(ii) f is one-to-one and g is one-to-one</p>
<p>Let A = {1, 2}, B = {a, b} and C = {α, β}.</p>
<p>Given f: A -> B where f(1) = a, f(2) = b and g: B -> C where g(a) = α, g(b) = α.</p>
<p>Then, gof: A -> C which gives g(f(1)) = g(a) = α and g(f(2)) = g(b) = β.</p>
<p>Here, g(f(1)) and g(f(2)) both gives α which implies that <strong>gof is one-to-one.</strong></p>
<p> </p>
<p>Are above examples correct? If yes, please explain.</p>Set Theory & Algebrahttps://gateoverflow.in/153066/function-compositionMon, 18 Sep 2017 05:31:28 +0000UGCNET-Dec2009-ii-01
https://gateoverflow.in/152685/ugcnet-dec2009-ii-01
If she is my friend and you are her friend, then we are friends. Given this, the friend relationship in this context is ____________.<br />
<br />
(i) commutative (ii) transitive (iii) implicative (iv) equivalence<br />
<br />
(A) (i) and (ii)<br />
<br />
(B) (iii)<br />
<br />
(C) (i), (ii), (iii) and (iv)<br />
<br />
(D) None of theseSet Theory & Algebrahttps://gateoverflow.in/152685/ugcnet-dec2009-ii-01Sat, 16 Sep 2017 14:19:29 +0000Function
https://gateoverflow.in/152643/function
How many onto function are there from a set with 5 element to a set with 4 elements?<br />
<br />
A. 340 B. 240 C. 440 D. 540Set Theory & Algebrahttps://gateoverflow.in/152643/functionSat, 16 Sep 2017 12:06:01 +0000number of strings
https://gateoverflow.in/152124/number-of-strings
COnsider a string of lngth 10 containing only 0 and 1<br />
<br />
the number of strings containg exactly 3 0's or 3 1's is ____________Set Theory & Algebrahttps://gateoverflow.in/152124/number-of-stringsThu, 14 Sep 2017 11:06:22 +0000relations
https://gateoverflow.in/152121/relations
a relation is defined as (a , b) R ( c , d) iff a=c or b=d<br />
<br />
is R antisymmetric ?Set Theory & Algebrahttps://gateoverflow.in/152121/relationsThu, 14 Sep 2017 11:00:25 +0000On sets
https://gateoverflow.in/152119/on-sets
Consider two sets A and B such that A U B is a subset of A intersection B<br />
<br />
the A={ } and B={ } is always true or falseSet Theory & Algebrahttps://gateoverflow.in/152119/on-setsThu, 14 Sep 2017 10:58:35 +0000Techhud
https://gateoverflow.in/151566/techhud
Find the total number of equivalent relations possible on a set S={4,7,1}?<br />
<br />
I am getting 8.Set Theory & Algebrahttps://gateoverflow.in/151566/techhudTue, 12 Sep 2017 08:16:02 +0000Discrete Mathematics
https://gateoverflow.in/151517/discrete-mathematics
Let G be a non abelian group, order of G can be<br />
<br />
A. 24<br />
<br />
B. 34<br />
<br />
C. 44<br />
<br />
D. 54Set Theory & Algebrahttps://gateoverflow.in/151517/discrete-mathematicsTue, 12 Sep 2017 05:31:12 +0000self doubt
https://gateoverflow.in/150994/self-doubt
<p>Consider the set N<sup>∗</sup> of finite sequences of natural numbers with x ≤<sub>p</sub> y denoting that sequence x is a prefix of sequence y. Then, which of the following is true?</p>
<table>
<thead>
<tr>
<th> </th>
<th> </th>
</tr>
</thead>
</table>
<table>
<thead>
<tr>
<th> </th>
<th> </th>
</tr>
</thead>
<tbody>
<tr>
<td> </td>
<td>
<p>Every non-empty subset of N<sup>∗</sup> has a least upper bound.</p>
</td>
</tr>
<tr>
<td> </td>
<td>
<p>N<sup>∗</sup> is uncountable.</p>
</td>
</tr>
<tr>
<td> </td>
<td>
<p>≤<sub>p</sub> is a total order.</p>
</td>
</tr>
<tr>
<td> </td>
<td>
<p>Every non-empty subset of N<sup>∗</sup> has a greatest lower bound.</p>
</td>
</tr>
</tbody>
</table>Set Theory & Algebrahttps://gateoverflow.in/150994/self-doubtSat, 09 Sep 2017 13:39:40 +0000set theory
https://gateoverflow.in/150902/set-theory
How many minimum number must be chosen from a set {1,2,3,...8} such that at least 2 of them must have sum=9?Set Theory & Algebrahttps://gateoverflow.in/150902/set-theorySat, 09 Sep 2017 09:26:05 +0000Linearity
https://gateoverflow.in/150674/linearity
Is this function is linear?<br />
<br />
f(X,Y,Z)=XY+X'Y'ZSet Theory & Algebrahttps://gateoverflow.in/150674/linearityFri, 08 Sep 2017 06:50:48 +0000Math on set theory
https://gateoverflow.in/150531/math-on-set-theory
The number of pairs of set (X,Y) are there that satisfy the condition $X,Y\subseteq \left \{ 1,2,3,4,5,6 \right \}$ and $X\cap Y=\Phi$________________Set Theory & Algebrahttps://gateoverflow.in/150531/math-on-set-theoryThu, 07 Sep 2017 16:36:25 +0000Random problem
https://gateoverflow.in/150287/random-problem
Let A = { a,b,c,d } which of the following is not true ?<br />
a) R1 = { (a,a) (c,c) } is Symmetric, Anti-Symmetric and Transitive on A<br />
b) R2 = { (a,b) (b,a) (a,c) (c,a) (c,d) } is Symmetric and Anti-Symmetric<br />
c) R3 = { (b,c) (c,b) (d,d) } is Symmetric but not Anti-Symmetric<br />
d) R4 = { (a,b) (b,c) (c,c) } is Anti-Symmetric but not SymmetricSet Theory & Algebrahttps://gateoverflow.in/150287/random-problemWed, 06 Sep 2017 14:52:57 +0000Set theory doubt
https://gateoverflow.in/150080/set-theory-doubt
<h3>Say if A is proper subset of B i.e <strong>A⊂B </strong>then is it true - </h3>
<h3>that <strong>B⊆A</strong> (B is subset of A)?</h3>
<p>Also one more thing - if <strong>A⊂B then AUB = A where U means UNION</strong></p>Set Theory & Algebrahttps://gateoverflow.in/150080/set-theory-doubtTue, 05 Sep 2017 13:43:45 +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 +0000group theory
https://gateoverflow.in/148654/group-theory
<p>Which book to follow for <strong>Group Theory</strong> ? </p>Set Theory & Algebrahttps://gateoverflow.in/148654/group-theoryWed, 30 Aug 2017 19:29:38 +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 +0000Discrete_poset
https://gateoverflow.in/146192/discrete_poset
<p>It took me a while to solve, any hack on this?</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=12263858780788222777"></p>Set Theory & Algebrahttps://gateoverflow.in/146192/discrete_posetMon, 21 Aug 2017 17:36:38 +0000Set theory lattice
https://gateoverflow.in/145957/set-theory-lattice
<p><img alt="Displaying IMG-20170821-WA0001.jpg" src="https://lh6.googleusercontent.com/hh6lxux3JiDVnC7pxgCJsxi0OFZLCqOVOweNd0YYYHv4zoIux1-kEAbFj6vnAvbbIHfWaYMzXdMmLqnHLR-BcgkPkXDYRJ6tK0Xe=w1304-h669-rw"></p>
<p> </p>
<p>why lub of 2 and 3 does not exist ... upper bond of 2 and 3 is 12 18 and 36 ... least among them is 12 thus least upper bond is 12... right?</p>
<p> </p>
<p>question image : <a rel="nofollow" href="https://drive.google.com/open?id=0ByxeyAYDQMMXakFLYTZ6NE9OWEtOSjQ1LXp5dmhGS0FiT3dF">https://drive.google.com/open?id=0ByxeyAYDQMMXakFLYTZ6NE9OWEtOSjQ1LXp5dmhGS0FiT3dF</a></p>
<p> </p>
<p> </p>Set Theory & Algebrahttps://gateoverflow.in/145957/set-theory-latticeMon, 21 Aug 2017 06:04:24 +0000Kenneth Rosen section 3.4 Exercise question 12
https://gateoverflow.in/145507/kenneth-rosen-section-3-4-exercise-question-12
<p>Is this approach right in proving a theorem </p>
<p><strong>Ques</strong>: show that a mod m = b mod m if a is congruent to b (mod m)</p>
<p><strong>Proof</strong>: given a is congruent to b(mod m)</p>
<p>According to definition:
<br>
a - b / m
<br>
i.e a - b = mx (for some integer x). ....(1)</p>
<p>Also a = mx + b
<br>
that can also be written as a mod m = b ...(2)</p>
<p>Also again from equation (1)</p>
<p>-b = mx - a
<br>
b = -mx + a
<br>
Or b = m(-x) + a
<br>
Or b = my + a ...(3)</p>
<p>Therefore b mod m = a </p>
<p>If we replace b in equation (2) by equation (3) then we get </p>
<p>a mod m = my + a
<br>
my + a can also be written as b mod m </p>
<p>Therefore, a mod m = b mod m </p>Set Theory & Algebrahttps://gateoverflow.in/145507/kenneth-rosen-section-3-4-exercise-question-12Sat, 19 Aug 2017 11:23:01 +0000Set Relation
https://gateoverflow.in/143337/set-relation
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=2897476246272035918" style="float:left"></p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=18400819236796253539" style="float:left"></p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<p>Answer please explain the ans.</p>
<p>R is antisymmetric then aRb, bRa -> a=b so a-b=0 and 0 is not odd positive then how it is antisymmetric?</p>Set Theory & Algebrahttps://gateoverflow.in/143337/set-relationFri, 11 Aug 2017 16:35:42 +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 +0000Gate CSE Web Link on Groups: Conceptual Doubt
https://gateoverflow.in/141380/gate-cse-web-link-on-groups-conceptual-doubt
<p>My question is about sub-groups.</p>
<p>I didn't understand how <strong><em>A non-empty subset H is a sub-group of a finite group G if and only if for all a belongs to H, b belongs to H, a*b belongs to H.</em></strong></p>
<p>For example, (⎨1, 1/2 and 2⎬, *) is a group on multiplication but H = ⎨1, 1/2 ⎬ is not a sub-group. This is because there is no inverse for 1/2 in H.</p>
<p>However, the PDF linked to on the Gate CSE site under 'Set Theory and Algebra' says:</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=450374964313683262"></p>
<p>Could someone please tell me what this means/how this is true?</p>Set Theory & Algebrahttps://gateoverflow.in/141380/gate-cse-web-link-on-groups-conceptual-doubtThu, 03 Aug 2017 06:23:43 +0000Discrete Maths Kenneth H. Rosen Ex 9.4 Relations
https://gateoverflow.in/141221/discrete-maths-kenneth-h-rosen-ex-9-4-relations
<p>Hi, following is a question from Kenneth H. Rosen :</p>
<p>Find the smallest relation containing the relation <strong>R ={(a, b) | a>b}</strong> that is both reﬂexive and symmetric?</p>
<p>The online solution given to the above problem is :</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=14535869392229778214"></p>
<p>I couldn't understand the given solution. Isn't the question asking just for the closure(which should be reflexive and symmetric) of the given relation? Can someone please help me understand this question? </p>Set Theory & Algebrahttps://gateoverflow.in/141221/discrete-maths-kenneth-h-rosen-ex-9-4-relationsWed, 02 Aug 2017 11:36:49 +0000Rosen 2.5.22
https://gateoverflow.in/140453/rosen-2-5-22
Suppose that A is a countable set. Show that the set B is also countable if there is an onto function f from A to B.Set Theory & Algebrahttps://gateoverflow.in/140453/rosen-2-5-22Sat, 29 Jul 2017 08:06:01 +0000#Relations
https://gateoverflow.in/140177/%23relations
No of relation over set of 4 elements such that (x,y) belongs to S implies (x=y)?<br />
<br />
Is it asking for reflexive relation?Set Theory & Algebrahttps://gateoverflow.in/140177/%23relationsThu, 27 Jul 2017 08:26:30 +0000#testbook
https://gateoverflow.in/140176/%23testbook
A one to one function from infinite set A to itself is one to one or not?<br />
<br />
A one to one function from finite set A to itself is one to one or not?<br />
<br />
Please suggest an approach to tackle these questions.Set Theory & Algebrahttps://gateoverflow.in/140176/%23testbookThu, 27 Jul 2017 08:23:59 +0000#Random_test
https://gateoverflow.in/140175/%23random_test
Group of students 100 students studying subject A,100 Subject B, 100 Subject C, 20 studying A&b, 40 B&C, and 60 A&C<br />
210 students are only studying one subject?<br />
<br />
Question : how many studying all three?Set Theory & Algebrahttps://gateoverflow.in/140175/%23random_testThu, 27 Jul 2017 08:22:13 +0000#random_question
https://gateoverflow.in/140173/%23random_question
Set A contains n elements.<br />
<br />
A largest relation on A which is both Symmetric and Antisymmetric?Set Theory & Algebrahttps://gateoverflow.in/140173/%23random_questionThu, 27 Jul 2017 08:19:14 +0000Rosen: Relations
https://gateoverflow.in/140015/rosen-relations
Draw the Venn Diagram Between Reflexive property, Symmetric property, and Anti-symmetric property?Set Theory & Algebrahttps://gateoverflow.in/140015/rosen-relationsWed, 26 Jul 2017 12:00:12 +0000Tremblay and Manohar
https://gateoverflow.in/139939/tremblay-and-manohar
S={2,a,{3},4} and R={{a},3,4,1} indicate whether the following are true or false<br />
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1) $\varnothing \subset R$<br />
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2)$\varnothing \subseteq \left \{ \left \{ a \right \} \right \}\subseteq R\subseteq E$ E=Universal Set<br />
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3) $\left \{ \varnothing \right \}\subseteq S$<br />
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4) $\varnothing \in R$<br />
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I think 1,2 are true and 3 is false and about 4 nothing is clearSet Theory & Algebrahttps://gateoverflow.in/139939/tremblay-and-manoharWed, 26 Jul 2017 05:57:09 +0000