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Recent questions in Set Theory & Algebra
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1
Infinite Descending Chain
From Wiki : Given a set S with a partial order ≤, an infinite descending chain is an infinite, strictly decreasing sequence of elements x1 > x2 > ... > xn > ... As an example, in the set of integers, the chain −1, ... used in number theory, while the latter is preferred in set theory and computer science. Now while solving question which definition to use ?
asked
6 days
ago
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Set Theory & Algebra
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Na462
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8
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discretemathematics
0
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2
Abstract algebra question
What is the maximal order of an element in S7? The symbol Sn will stand for the set of all permutations of the symbols {1,2,···,n}, which is a group under composition.
asked
Jun 13
in
Set Theory & Algebra
by
Forrest Gump
(
47
points)

10
views
settheory&algebra
algebra
0
votes
1
answer
3
ACE booklet
Please solv
asked
Jun 12
in
Set Theory & Algebra
by
Pradeep A
(
37
points)

41
views
0
votes
0
answers
4
ACE booklet
Please solve this
asked
Jun 12
in
Set Theory & Algebra
by
Pradeep A
(
37
points)

58
views
0
votes
0
answers
5
self doubt on previous year question
https://gateoverflow.in/8281/gate2015134 what is the exact probablity ? nd is question is saying to have a tuple in which atleast there should be one element who has only one complement to satisfy the given property?
asked
Jun 11
in
Set Theory & Algebra
by
eyeamgj
Active
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2.4k
points)

15
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0
votes
1
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6
ACE booklet
R be a set of real # and ( R, *) is a group with respect to operation a*b= a+b+2, then inverse of 2 is...... (a) 2 (b) 4 (c) 6 (d) 8
asked
Jun 11
in
Set Theory & Algebra
by
Pradeep A
(
37
points)

20
views
0
votes
2
answers
7
Distributive Lattice
Is below diagram is distributive lattice?
asked
Jun 9
in
Set Theory & Algebra
by
srestha
Veteran
(
86.9k
points)

111
views
lattice
discretemathematics
0
votes
1
answer
8
ACE Booklet
Let A ={ x  x belongs to R and x!= 2} B ={ x  x belongs to R and x!= 1} function f: A to B and function g: B to A f(x) = x/(x2) and g(x) = 2x/(x1) then which is false??? (a) fog = gof (b) fog = IB (c) f = g1 (d) fog is bijection
asked
Jun 9
in
Set Theory & Algebra
by
Pradeep A
(
37
points)

31
views
0
votes
1
answer
9
ACE que booklet
If the set has a finite # of elements, prove that if f maps S onto S1 then which of the following is false?? (a) f is 11 (b) f is onto (c) f is bijection (d) f is onto and not bijection
asked
Jun 9
in
Set Theory & Algebra
by
Pradeep A
(
37
points)

14
views
0
votes
0
answers
10
Self doubt regarding complete lattice related to https://gateoverflow.in/27341/tifr2014b16
asked
Jun 8
in
Set Theory & Algebra
by
Soumya29
Loyal
(
9.9k
points)

69
views
discretemathematics
settheory&algebra
lattice
0
votes
1
answer
11
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
Loyal
(
9.9k
points)

27
views
settheory&algebra
discretemathematics
relations
0
votes
2
answers
12
set theory
How many relation possible with $n$ elements of a set which are symmetric but not antisymmetric ?
asked
Jun 5
in
Set Theory & Algebra
by
Pradeep A
(
37
points)

37
views
engineeringmathematics
discretemathematics
settheory&algebra
0
votes
0
answers
13
Subset Doubt
I know it may be silly but, Say i have a set A = {1,2,3,4,5} then for subset we use ⊆ and for membership we use ∈. I can say 2 ∈ A , but 2 ⊆ A its wrong because 2 is an element of set its not a set. Can we Say {2} ⊆ A. ??? And for ϕ what to use : We know ϕ is a subset of every set So : ϕ ⊆ A. its correct right ? if its correct then ϕ ∈ A is it correct ?
asked
Jun 2
in
Set Theory & Algebra
by
Na462
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3.3k
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31
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discretemathematics
subset
0
votes
1
answer
14
Doubt
https://gateoverflow.in/25664/tifr2013b4 In this question i get it the answer is E. Plz check my reason : Since its a partial order relation because: we can relate every Xi << Xi itself and Its antisymmetric because no such pair Xi << Xi+1 ... if i choose any of the sequence it will always have a least element which will relate to everyone. Am i correct in my justification ?
asked
Jun 2
in
Set Theory & Algebra
by
Na462
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3.3k
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24
views
discretemathematics
0
votes
1
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15
Doubts About Lattices
Suppose Given a lattice i need to find how many pairs are there which will satisfy distributive property even though the given lattice is not distributive(becasue there exist atleast 1 element which has more than 1 complement ). How to solve such question. Say for example :
asked
May 31
in
Set Theory & Algebra
by
Na462
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3.3k
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22
views
discretemathematics
lattice
0
votes
1
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16
Isomorphic Groups
Can Please anybody describe the concept of Isomorphic Groups with an example ? Reference to https://gateoverflow.in/1219/gate200721
asked
May 31
in
Set Theory & Algebra
by
Na462
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3.3k
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42
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groups
0
votes
1
answer
17
Understanding points about countable sets from wikipedia
asked
May 30
in
Set Theory & Algebra
by
GateAspirant999
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2.5k
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56
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discretemathematics
settheory&algebra
0
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1
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18
Group theory
A homomorphism $f:G$ to $G1$ of groups is a monomorphism iff Ker $f = \{e\}$.
asked
May 29
in
Set Theory & Algebra
by
Sammohan Ganguly
(
417
points)

35
views
engineeringmathematics
discretemathematics
groups
grouphomomorphism
groupmonomorphism
0
votes
0
answers
19
selfdoubt
. Given a vector $x ∈ R_{n}$ , we define $xi=1$ , $P_{n}(i)=1....n$ $x_{i}  = x_{1} + x_{2} + x_{3} +.........x_{n} $and$ P_{n}( i) =1..........n$ $\sqrt{x_{1}^{2}+x_{2}^{2}+x_{3}^{2}....... ... The indices of all true (and no false) statements are (i) . (For example, if you think statements (a) and (b) are true and the rest false, write down (a),(b)' as your answer).
asked
May 27
in
Set Theory & Algebra
by
Kaluti
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5.4k
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29
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vector
0
votes
1
answer
20
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
Loyal
(
9.9k
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79
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discretemathematics
settheory&algebra
relations
0
votes
0
answers
21
The gate acadamy
[closed]
asked
May 21
in
Set Theory & Algebra
by
Bhavna kumrawat
(
35
points)

26
views
0
votes
0
answers
22
The gate acadamy
[closed]
asked
May 21
in
Set Theory & Algebra
by
Bhavna kumrawat
(
35
points)

33
views
0
votes
1
answer
23
NBHM exam
How many subgroups of order 2 are there in S4? The symbol Sn will stand for the set of all permutations of the symbols {1,2,···,n}, which is a group under composition.
asked
May 20
in
Set Theory & Algebra
by
Forrest Gump
(
47
points)

24
views
discretemathematics
settheory&algebra
0
votes
1
answer
24
Set Theory
How to distinguish between countably finite , countably infinite , uncountably infinite set? for reference see this ques:https://gateoverflow.in/36654/whysetofallfunctionsfn01isuncountablyinfinite
asked
May 15
in
Set Theory & Algebra
by
srestha
Veteran
(
86.9k
points)

114
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discretemathematics
settheory&algebra
settheory
sets
engineeringmathematics
0
votes
1
answer
25
Self Doubt. Related to https://gateoverflow.in/94634/gate198813ii#c216658.
asked
May 14
in
Set Theory & Algebra
by
Soumya29
Loyal
(
9.9k
points)

118
views
discretemathematics
settheory&algebra
functions
0
votes
1
answer
26
JNU exam
If R be an equivalence relation on the set, A={6,7,8,9,10} defined by, R={(6,6),(7,7),(8,8),(9,9),(10,10),(6,7),(7,6),(8,9),(9,8),(9,10),(10,9),(8,10),(10,8)}, its partitions are a) {{6},{7},{8,9},{10}} b) {{6,7,8},{9,10}} c) {{6},{7,8},{9,10}} d) {{6,7},{8,9,10}}
asked
May 14
in
Set Theory & Algebra
by
nepobose
(
13
points)

23
views
0
votes
1
answer
27
ISI 2018 PCB A4
Let A and B be two nonempty finite subsets of ℤ, the set of all integers. Define A + B = { a + b : a ϵ A, b ϵ B }. Prove that  A + B  ≥  A  +  B   1, where  S  denotes the cardinality of a finite set S.
asked
May 14
in
Set Theory & Algebra
by
tathatj
(
67
points)

65
views
settheory&algebra
userisi2018
usermod
+1
vote
1
answer
28
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
Boss
(
12.6k
points)

36
views
cmi2015
relations
settheory&algebra
+1
vote
1
answer
29
REGARDING SYLLABUS
ARE QUESTIONS ON FUZZY SET AND FUZZY RELATION IS IN GATE SYLLABUS OR NOT??????
asked
May 8
in
Set Theory & Algebra
by
eyeamgj
Active
(
2.4k
points)

40
views
+2
votes
0
answers
30
Related to gate 1989
Question related to http://gateoverflow.in/87051/gate19891v Binary Operation Cayley table. Can value repeat in particular Row or Column of Cayley table? In answer to above question they have mentioned that we can fill each element in n ways , If they can be filled in n ways values will definitely be repeat.
asked
May 8
in
Set Theory & Algebra
by
mehul vaidya
Junior
(
993
points)

60
views
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