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Recent questions and answers in Set Theory & Algebra
+2
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1
answer
1
Sequence
Conjecture a simple formula for an if the first few terms are 1,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4
answered
1 day
ago
in
Set Theory & Algebra
by
phani143
(
11
points)

105
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sequenceseries
0
votes
1
answer
2
Set Theory Self Doubt
Is the subset of a countably infinite set countable?
answered
3 days
ago
in
Set Theory & Algebra
by
Arjun
Veteran
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386k
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9
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0
votes
0
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3
Kenneth Rosen Edition 7th Exercise 2.2 Question 49 (Page No. 137)
Find ${\displaystyle \bigcup _{i=1}^{\infty }A_{i}} and \bigcup_{i=1}^{\infty} A_{i}$ if for every positive integer i, a) Ai = {i, i + 1, i + 2, . . .}. b) Ai = {0, i}. c) Ai = (0, i), that is, the set of real numbers x with 0 < x < i. d) Ai = (i,∞), that is, the set of real numbers x with x > i.
asked
5 days
ago
in
Set Theory & Algebra
by
sumitr
(
217
points)

9
views
kennethrosen
discretemathematics
0
votes
2
answers
4
Zeal Test Series 2019: Set Theory & Algebra  Relations
The Number of Relations, Which are both Reflexive and Symmetric but not AntiSymmetric, on a set with 6 elements, are ____________? i got 32768 plz check
answered
Mar 13
in
Set Theory & Algebra
by
abhishekmehta4u
Boss
(
29k
points)

53
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zeal
discretemathematics
settheory&algebra
relations
zeal2019
+2
votes
2
answers
5
Zeal Test Series 2019: Set Theory & Algebra  Relations
is there any shortcut to do this question fast ?
answered
Mar 13
in
Set Theory & Algebra
by
karan25gupta
(
67
points)

74
views
zeal
settheory&algebra
relations
zeal2019
0
votes
1
answer
6
ISIMMA201592
Consider the group $G \;=\; \begin{Bmatrix} \begin{pmatrix} a & b \\ 0 & a^{1} \end{pmatrix}\;: a,b \in \mathbb{R},a>0 \end{Bmatrix}$ ... order (D) $N$ is a normal subgroup and the quotient group is isomorphic to $\mathbb{R}^{+}$(the group of positive reals with multiplication).
answered
Mar 10
in
Set Theory & Algebra
by
srestha
Veteran
(
109k
points)

80
views
groups
groupisomorphism
engineeringmathematics
userisi2015
usermod
+1
vote
1
answer
7
Ace Test Series: Set Theory & Algebra  Relations
Let $A=\left \{ 1,2,3 \right \}$. Number of relation on $A$ which are neither reflexive, nor irreflexive but symmetric is ___________ Ans given 48 but I got 8 Please verify
answered
Mar 9
in
Set Theory & Algebra
by
Debdeep1998
Junior
(
597
points)

118
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acetestseries
engineeringmathematics
discretemathematics
settheory&algebra
relations
0
votes
2
answers
8
Ace Test Series: Set Theory & Algebra  Relations
Ans:B Symmetric closure of R 1. It is symmetric 2. It contains R 3.Minimal relation satisfying 1 and 2 If we consider B, then condition 2 may be violated. Therefore I think the answer should be D.
answered
Mar 9
in
Set Theory & Algebra
by
Debdeep1998
Junior
(
597
points)

96
views
acetestseries
settheory&algebra
relations
+18
votes
5
answers
9
GATE20082
If $P, Q, R$ are subsets of the universal set U, then $(P\cap Q\cap R) \cup (P^c \cap Q \cap R) \cup Q^c \cup R^c$ is $Q^c \cup R^c$ $P \cup Q^c \cup R^c$ $P^c \cup Q^c \cup R^c$ U
answered
Mar 9
in
Set Theory & Algebra
by
ShamikBanerjee
(
497
points)

1.6k
views
gate2008
normal
settheory&algebra
sets
0
votes
1
answer
10
General Topic Doubt Set Theory & Algebra: Relations
How to check a relation is transitive or not from its matrix representation? Please help me with an example.
answered
Mar 8
in
Set Theory & Algebra
by
saurav raghaw
Active
(
1.3k
points)

73
views
settheory&algebra
discretemathematics
relations
generaltopicdoubt
0
votes
1
answer
11
Relations
answered
Mar 7
in
Set Theory & Algebra
by
rajatmyname
Active
(
1.4k
points)

19
views
+1
vote
1
answer
12
Questions regarding Asymmetric relations. See Deatils.
Hello fellow folks, anyone may please explain these below questions  Ques 1  Relation Proper Subset ( ⊂ ) is it Asymmetric on set of all sets? Ques 2  Relation Subset ( ⊆ ) is it Asymmetric on set of all sets? ... Asymmetric on set of all sets? Kindly explain them in a simplified and with an illustrated example. Thank you in anticipation.
answered
Mar 7
in
Set Theory & Algebra
by
rajatmyname
Active
(
1.4k
points)

84
views
+1
vote
1
answer
13
Zeal Test Series 2019: Set Theory & Algebra  Lattice
I am getting 3 minimal please check it
answered
Mar 7
in
Set Theory & Algebra
by
abhishekmehta4u
Boss
(
29k
points)

86
views
discretemathematics
settheory&algebra
lattice
zeal
zeal2019
0
votes
1
answer
14
Rosen,Ch:9,Ex:9.3,Q10
answered
Mar 4
in
Set Theory & Algebra
by
prashant jha 1
Active
(
4.7k
points)

56
views
+27
votes
5
answers
15
GATE2016226
A binary relation $R$ on $\mathbb{N} \times \mathbb{N}$ is defined as follows: $(a, b) R(c, d)$ if $a \leq c$ or $b \leq d$. Consider the following propositions: $P:$ $R$ is reflexive. $Q:$ $R$ is transitive. Which one of the following statements is TRUE? Both $P$ and $Q$ are true. $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are false.
answered
Mar 2
in
Set Theory & Algebra
by
prashant jha 1
Active
(
4.7k
points)

4k
views
gate20162
settheory&algebra
relations
normal
0
votes
0
answers
16
Lattice (ACE)
Let $A=\left \{ 1,2,3 \right \}$. A relation $R$ on $A\times A$ is defined by $\left ( a,b \right )R\left ( c,d \right )\Leftrightarrow \left ( “a\leq c “and” b\leq d “\right )$ S1:$R$ partial order S2: The poset $\left [ A\times A:R \right ]$ is a lattice Among S1 and S2 which one is true?
asked
Feb 27
in
Set Theory & Algebra
by
srestha
Veteran
(
109k
points)

159
views
lattice
discretemathematics
+2
votes
1
answer
17
kenneth rosen Ex2.4 Q.46
Show that the set of functions from the positive integers to the set {0,1,2,3,4,5,6,7,8,9} is uncountable.
answered
Feb 21
in
Set Theory & Algebra
by
Devshree Dubey
Boss
(
13.6k
points)

137
views
+1
vote
1
answer
18
ISI MMA201527
Let, $cos^{6}\theta = a_{6}cos6\theta + a_{5}cos5\theta + a_{4}cos4\theta + a_{3}cos3\theta + a_{2}cos2\theta + a_{1}cos\theta + a_{0}$ Then $a_{0}$ is (A) $0$ (B) $\frac{1}{32}$ (C) $\frac{15}{32}$ (D) $\frac{10}{32}$ ... 3 equations , I am getting $a_{0} + a_{4} = \frac{1}{2}$ but don't know how to proceed further to get the value of $a_{0}$. Please help.
answered
Feb 21
in
Set Theory & Algebra
by
venkatesh pagadala
(
471
points)

113
views
engineeringmathematics
userisi2015
usermod
0
votes
1
answer
19
Kenneth Rosen Edition 6th Exercise 2.3 Question 36 (Page No. 147)
Let f be a function from the set A to the set B.Let S and T be subsets of A.Show that $f(S\cup T)=f(S)\cup f(T)$ $f(S\cap T)\subseteq f(S)\cap f(T)$ Show that inclusion in part b can be proper
answered
Feb 19
in
Set Theory & Algebra
by
prashant jha 1
Active
(
4.7k
points)

63
views
kennethrosen
settheory&algebra
discretemathematics
0
votes
1
answer
20
kenneth rosen Ex 2.3 Q.29,30
Justify the statements. 1. if f and f o g are one to one,does it follows that g is one to one. 2 if f and f o g are onto,does it follow that g is onto
answered
Feb 18
in
Set Theory & Algebra
by
Deepakk Poonia (Dee)
Boss
(
23.4k
points)

33
views
–1
vote
0
answers
21
Kenneth Rosen Ex.2.3 Q.3(c)
https://prnt.sc/cncgcv plz explain the c part!
asked
Feb 18
in
Set Theory & Algebra
by
himgta
Active
(
3.8k
points)

69
views
+1
vote
0
answers
22
JEST 2019
Let ${(0,1)}^n$ set of all binary string of length n. Hamming sphere of radius around a string C in ${(0,1)}^n$ is the set of all strings d$\epsilon$ ${(0,1)}^n$ that differ from C in at most r of n position, S(C,r) for n=2k+1 For C,C’ $\epsilon$ ${(0,1)}^n$ S(C,k) and S(C’,k) are disjoint couldn't remember rest of the options.
asked
Feb 17
in
Set Theory & Algebra
by
vivek_mishra
(
401
points)

60
views
jest
2019
discretemathematics
0
votes
0
answers
23
JEST 2019 Descriptive Q3 (8 Marks)
Determine the number of functions f:{1,2,3…,n}→{1995,1996} satisfying the condition that f(1)+f(2)+…f(n) is odd.
asked
Feb 17
in
Set Theory & Algebra
by
dan31
Junior
(
689
points)

80
views
jest2019
discretemathematics
+1
vote
2
answers
24
TIFR2011MathsA16
The polynomial $x^{4}+7x^{3}13x^{2}+11x$ has exactly one real root.
answered
Feb 16
in
Set Theory & Algebra
by
Sreyasree Mandal
(
117
points)

123
views
tifrmaths2011
polynomials
+2
votes
1
answer
25
JEST Sample Question 1b
When is the following statement true? (A ∪ B) ∩ C = A ∩ C (A) If Ā ∩ B ∩ C = φ (B) If A ∩ B ∩ C = φ (C) always (D) never
answered
Feb 15
in
Set Theory & Algebra
by
Ram Swaroop
Active
(
2.5k
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66
views
jest
discretemathematics
settheory&algebra
0
votes
1
answer
26
JEST Sample Question 1a
Let a and b be positive integers such that a > b and a^ 2 − b^ 2 is a prime number. Then a^2 − b^ 2 is equal to (A) a − b (B) a + b (C) a × b (D) none of the above
answered
Feb 15
in
Set Theory & Algebra
by
Naveen Kumar 3
Loyal
(
6.2k
points)

65
views
jest
discretemathematics
settheory&algebra
0
votes
1
answer
27
Jest Exam sample question3
How many subsets of even cardinality does an nelement set have ? Justify answer. Please give a proof if possible.This is part of subjective JEST paper.
answered
Feb 15
in
Set Theory & Algebra
by
subhrob
(
373
points)

23
views
jest
settheory&algebra
discretemathematics
+2
votes
4
answers
28
GATE201910
Let $G$ be an arbitrary group. Consider the following relations on $G$: $R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a = g^{1}bg$ $R_2: \forall a , b \in G, \: a R_2 b \text{ if and only if } a= b^{1}$ Which of the above is/are equivalence relation/relations? $R_1$ and $R_2$ $R_1$ only $R_2$ only Neither $R_1$ nor $R_2$
answered
Feb 10
in
Set Theory & Algebra
by
amangarg
(
63
points)

2k
views
gate2019
engineeringmathematics
discretemathematics
settheory&algebra
groups
+2
votes
3
answers
29
GATE 2019
Let U = {1, 2, ..., n} and A = {(x, X), x ∈ X and X ⊆ U}. Consider the following two statements for A. (i) A = n*$\small 2^{n1}$ (ii) A= Sigma(k=1 to n) k.(nCk) Which of the following is correct? (a) (i) only (b) (ii) only (c) Both (i) and (ii) (d) None of the above
answered
Feb 6
in
Set Theory & Algebra
by
Ahabnnc
Junior
(
977
points)

547
views
0
votes
0
answers
30
#math
asked
Feb 5
in
Set Theory & Algebra
by
Sankha Narayan Bose
Junior
(
745
points)

102
views
gate19
0
votes
3
answers
31
GATE 2019: Equivalent Relation
Which of the following equivalent relation of a group G? R 1 : ∀ a , b ∈ G , a R 1 b if only ∃ g ∈ G : a = g − 1 bg R 2 : ∀ a , b ∈ G , a R 2 b if only a = b –1 (a) Both R 1 and R 2 (c) R 1 (b) R 2 (d) None of these
answered
Feb 4
in
Set Theory & Algebra
by
pream sagar
Active
(
1.7k
points)

271
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relations
0
votes
2
answers
32
Gate 2019
What is the for the question where two statements were given as: S1: matrix A is invertible S2:A=0?
answered
Feb 4
in
Set Theory & Algebra
by
Shashi Shekhar 1
Junior
(
681
points)

257
views
0
votes
0
answers
33
ME FLT5
Consider the following POSETs: Which of the above POSETs are isomorphic to (P (S), ⊆), where S = {a, b, c}?
asked
Jan 30
in
Set Theory & Algebra
by
balchandar reddy san
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(
2.7k
points)

71
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engineeringmathematics
0
votes
1
answer
34
GATEBOOK2019 Mock Test136
Which of the following statements is/are TRUE? $A \cup (B − C)$ always equals $ (A \cup B) − (A \cup C) $ $A \cap (B − C) $ always equals $(A \cap B) − (A \cap C) $ $A − (B \cap C) $ always equals $(A − B) \cup (A − C) $ $I$ only $I$ and $II$ only $II$ and $III$ only $I, II,$ and $III$
answered
Jan 30
in
Set Theory & Algebra
by
Shaik Masthan
Veteran
(
57.6k
points)

103
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gb2019mock1
sets
discretemathematics
+1
vote
1
answer
35
MadeEasy Test Series 2019: Discrete Mathematics  Set Theory & Algebra
Which of the following are Well ordered set $\left [ Z^{+},\leq \right ]$ $\left [ Z^{},\leq \right ]$ $\left [ Z^{+},\geq \right ]$ $\left [ Z^{},\geq \right ]$
answered
Jan 28
in
Set Theory & Algebra
by
_sonu
(
221
points)

138
views
madeeasytestseries
settheory&algebra
0
votes
0
answers
36
made easy test series
What is the number of generators in a group G, such that Ο(G) = 87?
asked
Jan 26
in
Set Theory & Algebra
by
pream sagar
Active
(
1.7k
points)

142
views
0
votes
1
answer
37
MadeEasy Test Series: Set Thoery & Algebra  Partial Order
Let Q denote the set of rational numbers and S = {x  x belongs N ; N; x>=10} Consider the Following POSETs I. (Q ∩ [0, 1], ≤) II. (S, ≤) Which of the above POSETs are well ordered?
answered
Jan 26
in
Set Theory & Algebra
by
Na462
Loyal
(
8.7k
points)

112
views
settheory&algebra
partialorder
madeeasytestseries
0
votes
1
answer
38
Ace Test Series question
Ans is given B but my question is why option D is wrong.
answered
Jan 26
in
Set Theory & Algebra
by
Meet2698
(
143
points)

28
views
0
votes
1
answer
39
GATE2018ECE
Let M be a real 4 × 4 matrix. Consider the following statements : S1 : M has 4 linearly independent eigenvectors. S2 : M has 4 distinct eigenvalues. S3 : M is nonsingular (invertible). Whict one among the following is TRUE? (a) S1 implies S2 (b) S2 implies S1 (c) S1 implies S3 (d) S3 implies S2 Note: Plz explain in detail why other options are incorrect.
answered
Jan 26
in
Set Theory & Algebra
by
Barney Ross
(
235
points)

254
views
0
votes
0
answers
40
Made Easy
[closed]
asked
Jan 25
in
Set Theory & Algebra
by
anjali007
Loyal
(
5.4k
points)

54
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