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Recent questions and answers in Set Theory & Algebra
+3
votes
1
answer
1
Mock DFS Q
Consider DFS over undirected graph with 4 vertices <A;B;C;D>. The discovery and finishing times of them in the order A to D are given. Select the option from following showing more than one connected components: 1) <(1,6), (2,5), (3,4), (8,10)> 2) <(6,7), (2,5), (3,4), (8,9)> 3) <(4,5), (2,8), (1,7), (3,6)> 4) <(7,8), (1,2), (5,6), (3,4)>
answered
2 days
ago
in
Set Theory & Algebra
by
vk82942349
(
11
points)

126
views
+31
votes
5
answers
2
GATE200624
Given a set of elements N = {1, 2, ..., n} and two arbitrary subsets A⊆N and B⊆N, how many of the n! permutations $\pi$ from N to N satisfy min($\pi$(A)) = min($\pi$(B)), where min(S) is the smallest integer in the set of integers S, and $\pi$(S) is the set of integers obtained by applying ... $n! \frac{A ∩ B}{A ∪ B}$ $\dfrac{A ∩ B^2}{^n \mathrm{C}_{A ∪ B}}$
answered
Nov 7
in
Set Theory & Algebra
by
Sourajit25
Active
(
1.2k
points)

2.9k
views
gate2006
settheory&algebra
normal
sets
+1
vote
2
answers
3
GATE20014
Consider the function $h: N \times N \rightarrow N$ so that $h(a,b) = (2a +1)2^b  1$, where $N=\{0,1,2,3,\dots\}$ is the set of natural numbers. Prove that the function $h$ is an injection (oneone). Prove that it is also a Surjection (onto)
answered
Nov 6
in
Set Theory & Algebra
by
mohan123
Active
(
1.2k
points)

407
views
gate2001
functions
settheory&algebra
normal
descriptive
0
votes
1
answer
4
Hasse Doubt
what is the least upper bound of {a, b, c}?
answered
Nov 4
in
Set Theory & Algebra
by
gorya506
(
201
points)

88
views
hassediagram
settheory&algebra
lattice
partialorder
+21
votes
5
answers
5
GATE201827
Let $N$ be the set of natural numbers. Consider the following sets, $P:$ Set of Rational numbers (positive and negative) $Q:$ Set of functions from $\{0,1\}$ to $N$ $R:$ Set of functions from $N$ to $\{0, 1\}$ $S:$ Set of finite subsets of $N$ Which of the above sets are countable? $Q$ and $S$ only $P$ and $S$ only $P$ and $R$ only $P, Q$ and $S$ only
answered
Oct 19
in
Set Theory & Algebra
by
JashanArora
Active
(
1.1k
points)

4.7k
views
gate2018
settheory&algebra
countableuncountableset
normal
+1
vote
2
answers
6
ISI2015MMA7
Let $X$ be the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \}$. Define the set $\mathcal{R}$ by $\mathcal{R} = \{(x,y) \in X \times X : x$ and $y$ have the same remainder when divided by $3\}$. Then the number of elements in $\mathcal{R}$ is $40$ $36$ $34$ $33$
answered
Oct 19
in
Set Theory & Algebra
by
chirudeepnamini
Active
(
2.5k
points)

15
views
isi2015mma
settheory
cartesianproduct
+1
vote
2
answers
7
set theory
answered
Oct 19
in
Set Theory & Algebra
by
Spidey_guy
(
115
points)

51
views
settheory&algebra
discretemathematics
engineeringmathematics
sets
+51
votes
7
answers
8
GATE2016228
Consider a set $U$ of $23$ different compounds in a chemistry lab. There is a subset $S$ of $U$ of $9$ compounds, each of which reacts with exactly $3$ compounds of $U$. Consider the following statements: Each compound in U \ S reacts with an odd number ... in U \ S reacts with an even number of compounds. Which one of the above statements is ALWAYS TRUE? Only I Only II Only III None.
answered
Oct 19
in
Set Theory & Algebra
by
Spidey_guy
(
115
points)

4.9k
views
gate20162
settheory&algebra
difficult
sets
+1
vote
2
answers
9
ISI2015MMA5
A set contains $2n+1$ elements. The number of subsets of the set which contain at most $n$ elements is $2^n$ $2^{n+1}$ $2^{n1}$ $2^{2n}$
answered
Oct 9
in
Set Theory & Algebra
by
techbd123
Active
(
2.6k
points)

35
views
isi2015mma
settheory
subsets
+1
vote
1
answer
10
ISI2014DCG15
Let $\mathbb{N}=\{1,2,3, \dots\}$ be the set of natural numbers. For each $n \in \mathbb{N}$, define $A_n=\{(n+1)k, \: k \in \mathbb{N} \}$. Then $A_1 \cap A_2$ equals $A_3$ $A_4$ $A_5$ $A_6$
answered
Oct 8
in
Set Theory & Algebra
by
techbd123
Active
(
2.6k
points)

29
views
isi2014dcg
settheory
algebra
0
votes
1
answer
11
ISI2014DCG35
Let $A$ and $B$ be disjoint sets containing $m$ and $n$ elements respectively, and let $C=A \cup B$. Then the number of subsets $S$ (of $C$) which contains $p$ elements and also has the property that $S \cap A$ contains $q$ ... $\begin{pmatrix} m \\ pq \end{pmatrix} \times \begin{pmatrix} n \\ q \end{pmatrix}$
answered
Oct 7
in
Set Theory & Algebra
by
techbd123
Active
(
2.6k
points)

16
views
isi2014dcg
settheory
disjointsets
+3
votes
2
answers
12
TIFR2010MathsA1
A cyclic group of order 60 has 12 Generators 15 Generators 16 Generators 20 Generators
answered
Oct 6
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Veteran
(
53.4k
points)

967
views
tifrmaths2010
groups
+2
votes
3
answers
13
TIFR2014MathsB4
Let $H_{1}$, $H_{2}$ be two distinct subgroups of a finite group $G$, each of order $2$. Let $H$ be the smallest subgroup containing $H_{1}$ and $H_{2}$. Then the order of $H$ is Always 2 Always 4 Always 8 None of the above.
answered
Oct 5
in
Set Theory & Algebra
by
Harry Richie
(
17
points)

337
views
tifrmaths2014
settheory&algebra
groups
0
votes
1
answer
14
ISI2015MMA93
Let $G$ be a group with identity element $e$. If $x$ and $y$ are elements in $G$ satisfying $x^5y^3=x^8y^5=e$, then which of the following conditions is true? $x=e, \: y=e$ $x\neq e, \: y=e$ $x=e, \: y \neq e$ $x\neq e, \: y \neq e$
answered
Oct 5
in
Set Theory & Algebra
by
shafique
(
17
points)

8
views
isi2015mma
grouptheory
groups
0
votes
1
answer
15
ISI2015MMA94
Let $G$ be the group $\{\pm1, \pm i \}$ with multiplication of complex numbers as composition. Let $H$ be the quotient group $\mathbb{Z}/4 \mathbb{Z}$. Then the number of nontrivial group homomorphisms from $H$ to $G$ is $4$ $1$ $2$ $3$
answered
Oct 5
in
Set Theory & Algebra
by
shafique
(
17
points)

9
views
isi2015mma
groups
quotientgroups
nongate
+1
vote
1
answer
16
TIFR2014MathsA15
How many proper subgroups does the group $\mathbb{Z} ⊕ \mathbb{Z}$ have? $1$ $2$ $3$ Infinitely many
answered
Oct 5
in
Set Theory & Algebra
by
Harry Richie
(
17
points)

191
views
tifrmaths2014
groups
+13
votes
2
answers
17
GATE201529
The number of divisors of $2100$ is ____.
answered
Oct 3
in
Set Theory & Algebra
by
JashanArora
Active
(
1.1k
points)

3.2k
views
gate20152
settheory&algebra
numbertheory
easy
numericalanswers
+5
votes
2
answers
18
GATE199525b
Determine the number of positive integers $(\leq 720)$ which are not divisible by any of $2,3$ or $5.$
answered
Sep 27
in
Set Theory & Algebra
by
techbd123
Active
(
2.6k
points)

281
views
gate1995
settheory&algebra
numericalanswers
sets
0
votes
1
answer
19
Kenneth Rosen Edition 7th Exercise 2.2 Question 14 (Page No. 136)
Find the sets $A$ and $B$ if $AB=\left \{ 1,5,7,8 \right \}, BA=\left \{ 2,10 \right \},$ and $A \cap B=\left \{ 3,6,9 \right \}.$
answered
Sep 24
in
Set Theory & Algebra
by
anurag_cs
(
53
points)

17
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
2
answers
20
SelfDoubt:Mathematical logic
“Every asymmetric relation is antisymmetric” Is this statement is True or False? I think it is false, because asymmetric relation never allows loops and antisymmetric relation allows loops. Am I not correct?
answered
Sep 24
in
Set Theory & Algebra
by
anurag_cs
(
53
points)

35
views
discretemathematics
0
votes
0
answers
21
ISI2015MMA23
Let $X$ be a nonempty set and let $\mathcal{P}(X)$ denote the collection of all subsets of $X$. Define $f: X \times \mathcal{P}(X) \to \mathbb{R}$ by $f(x,A)=\begin{cases} 1 & \text{ if } x \in A \\ 0 & \text{ if } x \notin A \end{cases}$ Then $f(x, A \cup B)$ ... $f(x,A)+f(x,B)\:  f(x,A) \cdot f(x,B)$ $f(x,A)\:+ \mid f(x,A)\:  f(x,B) \mid $
asked
Sep 23
in
Set Theory & Algebra
by
Arjun
Veteran
(
423k
points)

4
views
isi2015mma
settheory
functions
nongate
0
votes
0
answers
22
ISI2015MMA31
Consider the sets defined by the real solutions of the inequalities $A = \{(x,y):x^2+y^4 \leq 1 \} \:\:\:\:\:\:\:\: B = \{ (x,y):x^4+y^6 \leq 1\}$ Then $B \subseteq A$ $A \subseteq B$ Each of the sets $A – B, \: B – A$ and $A \cap B$ is nonempty none of the above
asked
Sep 23
in
Set Theory & Algebra
by
Arjun
Veteran
(
423k
points)

6
views
isi2015mma
settheory
nongate
0
votes
0
answers
23
ISI2015MMA92
Consider the group $G=\begin{Bmatrix} \begin{pmatrix} a & b \\ 0 & a^{1} \end{pmatrix} : a,b \in \mathbb{R}, \: a>0 \end{Bmatrix}$ ... is of finite order $N$ is a normal subgroup and the quotient group is isomorphic to $\mathbb{R}^+$ (the group of positive reals with multiplication).
asked
Sep 23
in
Set Theory & Algebra
by
Arjun
Veteran
(
423k
points)

9
views
isi2015mma
grouptheory
subgroups
normal
nongate
0
votes
1
answer
24
ISI2017DCG12
Two sets have $m$ and $n$ elements. The number of subsets of the first set is $96$ more than that of the second set. Then the values of $m$ and $n$ are $8$ and $6$ $7$ and $6$ $7$ and $5$ $6$ and $5$
answered
Sep 21
in
Set Theory & Algebra
by
Ashwani Kumar 2
Boss
(
15.5k
points)

6
views
isi2017dcg
settheory
sets
+1
vote
1
answer
25
ISI2015DCG36
Suppose $X$ and $Y$ are finite sets, each with cardinality $n$. The number of bijective functions from $X$ to $Y$ is $n^n$ $n \log_2 n$ $n^2$ $n!$
answered
Sep 21
in
Set Theory & Algebra
by
Satbir
Boss
(
20.7k
points)

14
views
isi2015dcg
settheory
functions
0
votes
1
answer
26
ISI2015DCG35
Let $A$, $B$ and $C$ be three non empty sets. Consider the two relations given below: $\begin{array}{lll} A(BC)=(AB) \cup C & & (1) \\ A – (B \cup C) = (A B)C & & (2) \end{array}$ Both $(1)$ and $(2)$ are correct $(1)$ is correct but $(2)$ is not $(2)$ is correct but $(1)$ is not Both $(1)$ and $(2)$ are incorrect
answered
Sep 21
in
Set Theory & Algebra
by
Satbir
Boss
(
20.7k
points)

8
views
isi2015dcg
settheory
sets
0
votes
1
answer
27
ISI2015DCG27
If $A$ be the set of triangles in a plane and $R^{+}$ be the set of all positive real numbers, then the function $f\::\:A\rightarrow R^{+},$ defined by $f(x)=$ area of triangle $x,$ is oneone and into oneone and onto manyone and onto manyone and into
answered
Sep 21
in
Set Theory & Algebra
by
`JEET
Boss
(
11.3k
points)

18
views
isi2015dcg
functions
triangles
+17
votes
6
answers
28
GATE199810a
Prove by induction that the expression for the number of diagonals in a polygon of $n$ sides is $\frac{n(n3)}{2}$
answered
Sep 20
in
Set Theory & Algebra
by
Gaurav Yadav
(
261
points)

1.2k
views
gate1998
settheory&algebra
descriptive
relations
+10
votes
3
answers
29
GATE199714
Let $R$ be a reflexive and transitive relation on a set $A$. Define a new relation $E$ on $A$ as $E=\{(a, b) \mid (a, b) \in R \text{ and } (b, a) \in R \}$ Prove that $E$ is an equivalence relation on $A$. Define a relation $\leq$ on the equivalence classes of $E$ ... $\exists a, b$ such that $a \in E_1, b \in E_2 \text{ and } (a, b) \in R$. Prove that $\leq$ is a partial order.
answered
Sep 19
in
Set Theory & Algebra
by
Sambhrant Maurya
Active
(
3.3k
points)

856
views
gate1997
settheory&algebra
relations
normal
proof
descriptive
0
votes
0
answers
30
ISI2015DCG37
Suppose $f_{\alpha} : [0,1] \to [0,1],\:\: 1 < \alpha < \infty$ is given by $f_{\alpha} (x) = \frac{(\alpha +1)x}{\alpha x+1}$ Then $f_{\alpha}$ is A bijective (oneone and onto) function A surjective (onto ) function An injective (oneone) function We cannot conclude about the type
asked
Sep 18
in
Set Theory & Algebra
by
gatecse
Boss
(
16.6k
points)

14
views
isi2015dcg
settheory
functions
+15
votes
4
answers
31
GATE19943.8
Give a relational algebra expression using only the minimum number of operators from $(∪, −)$ which is equivalent to $R$ $∩$ $S.$
answered
Sep 18
in
Set Theory & Algebra
by
Anurag007
(
11
points)

852
views
gate1994
settheory&algebra
normal
sets
descriptive
+20
votes
4
answers
32
GATE19968
Let $F$ be the collection of all functions $f: \{1, 2, 3\} \to \{1, 2, 3\}$. If $f$ and $g \in F$, define an equivalence relation $\sim$ by $f\sim g$ if and only if $f(3) = g(3)$. Find the number of equivalence classes defined by $\sim$. Find the number of elements in each equivalence class.
answered
Sep 10
in
Set Theory & Algebra
by
Debargha Bhattacharj
Junior
(
693
points)

1.7k
views
gate1996
settheory&algebra
relations
functions
normal
descriptive
+1
vote
1
answer
33
REGARDING DISCRETE MATHS SYLLABUS
FIELD AND RING ARE IN SYLLABUS???
answered
Sep 10
in
Set Theory & Algebra
by
Arjun
Veteran
(
423k
points)

106
views
+2
votes
2
answers
34
UGCNETDec2012II4
The power set of the set $\{ \Phi \}$ is $\{ \Phi \}$ $\{ \Phi, \{ \Phi \} \}$ $\{ 0 \}$ $\{ 0, \Phi , \{ \Phi \} \}$
answered
Sep 9
in
Set Theory & Algebra
by
omsanchitjain
(
33
points)

498
views
ugcnetdec2012ii
settheory&algebra
sets
powerset
+2
votes
3
answers
35
UGCNETDec2015II3
Which of the following is/are not true ? The set of negative integers is countable. The set of integers that are multiples of 7 is countable. The set of even integers is countable. The set of real numbers between 0 and 1⁄2 is countable. a and c b and d b only d only
answered
Sep 9
in
Set Theory & Algebra
by
omsanchitjain
(
33
points)

742
views
ugcnetdec2015ii
discretemathematics
settheory
+2
votes
1
answer
36
Countable and Uncountable Self Doubt 2
Which of the following is always correct? A. Cross product of two countable set is countable B. Cross product of two countable set is uncountable C. Cross product of two uncountable set is countable D. Cross product of uncountable ... E. Cross product of uncountable and countable set is countable F. Cross product of uncountable and countable set is uncountable
answered
Sep 5
in
Set Theory & Algebra
by
Sandee
(
11
points)

100
views
theoryofcomputation
countableuncountableset
settheory&algebra
+6
votes
3
answers
37
UGCNETJune2019II1
Consider the poset $( \{3,5,9,15,24,45 \}, \mid).$ Which of the following is correct for the given poset ? There exist a greatest element and a least element There exist a greatest element but not a least element There exist a least element but not a greatest element There does not exist a greatest element and a least element
answered
Sep 4
in
Set Theory & Algebra
by
bhupendrakumar
(
47
points)

579
views
ugcnetjune2019ii
poset
settheory&algebra
+1
vote
2
answers
38
isro exam december 2017
The number of elements in the power set of {{1,2},{2,1,1},{2,1,1,2}} is:
answered
Sep 1
in
Set Theory & Algebra
by
GoalSet1
(
191
points)

545
views
isro2017
+45
votes
4
answers
39
GATE200625
Let $S = \{1, 2, 3,\ldots, m\}, m >3.$ Let $X_1,\ldots,X_n$ be subsets of $S$ each of size $3.$ Define a function $f$ from $S$ to the set of natural numbers as, $f(i)$ is the number of sets $X_j$ that contain the element $i.$ That is $f(i)=\left  \left\{j \mid i\in X_j \right\} \right$ then $ \sum_{i=1}^{m} f(i)$ is: $3m$ $3n$ $2m+1$ $2n+1$
answered
Aug 27
in
Set Theory & Algebra
by
JashanArora
Active
(
1.1k
points)

2.6k
views
gate2006
settheory&algebra
normal
functions
+29
votes
10
answers
40
GATE2015240
The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.
answered
Aug 26
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Veteran
(
53.4k
points)

7.7k
views
gate20152
settheory&algebra
functions
normal
numericalanswers
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