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Recent questions and answers in Set Theory & Algebra
32
votes
4
answers
1
GATE CSE 1992 | Question: 14a
If $G$ is a group of even order, then show that there exists an element $a≠e$, the identity in $G$, such that $a^2 = e$.
Shubhamishere
answered
in
Set Theory & Algebra
9 hours
ago
by
Shubhamishere
5.7k
views
gate1992
set-theory&algebra
group-theory
normal
descriptive
proof
16
votes
4
answers
2
GATE CSE 1998 | Question: 1.6
Suppose $A$ is a finite set with $n$ elements. The number of elements in the largest equivalence relation of A is $n$ $n^2$ $1$ $n+1$
Roshan_Ace
answered
in
Set Theory & Algebra
Mar 21
by
Roshan_Ace
7.9k
views
gate1998
set-theory&algebra
relations
easy
0
votes
1
answer
3
set theory
If A = {1, 2, 3, . . . . . . 10} then the number of 4 element subsets of A containing ‘2’?
[ Jiren ]
answered
in
Set Theory & Algebra
Feb 28
by
[ Jiren ]
108
views
set-theory
2
votes
1
answer
4
GATE CSE 2023 | Question: 39
Let $f: A \rightarrow B$ be an onto (or surjective) function, where $A$ and $B$ are nonempty sets. Define an equivalence relation $\sim$ on the set $A$ as \[ a_{1} \sim a_{2} \text { if } f\left(a_{1}\right)=f\left(a_{2}\right), \] ... is NOT well-defined. $F$ is an onto (or surjective) function. $F$ is a one-to-one (or injective) function. $F$ is a bijective function.
ankitgupta.1729
answered
in
Set Theory & Algebra
Feb 16
by
ankitgupta.1729
897
views
gatecse-2023
set-theory&algebra
equivalence-class
multiple-selects
2-marks
2
votes
1
answer
5
GATE CSE 2023 | Question: 41
Let $X$ be a set and $2^{X}$ denote the powerset of $X$. Define a binary operation $\Delta$ on $2^{X}$ as follows: \[ A \Delta B=(A-B) \cup(B-A) \text {. } \] Let $H=\left(2^{X}, \Delta\right)$. Which of the following statements about $H$ is/are correct? ... $A \in 2^{X},$ the inverse of $A$ is the complement of $A$. For every $A \in 2^{X},$ the inverse of $A$ is $A$.
ankitgupta.1729
answered
in
Set Theory & Algebra
Feb 15
by
ankitgupta.1729
1.0k
views
gatecse-2023
set-theory&algebra
group-theory
multiple-selects
2-marks
0
votes
0
answers
6
Discrete Mathematics & Its Applications. Basic Structures - Sets, Functions, Sequences and Sums
N = {0,1,2,3 .} is the set of natural numbers. In Note, it is mentioned that some people do not consider 0 as a natural number. We know that set of Whole numbers is W = {0,1,2,3.. ... we consider 0 as an element in the set of Natural numbers, then what is the definition of Whole numbers in that scenario?
UdynGP
asked
in
Set Theory & Algebra
Feb 15
by
UdynGP
146
views
1
vote
2
answers
7
GATE CSE 2023 | Memory Based Question: 17
Let $x$ be a set, $2^x=$ power $2 \mathrm{k}$ set of $\mathrm{X}$. define A binary operation $\Delta$ on $2^x$ as $A \Delta B=(A-B) \cup(B-A)$. Let $H=\left(2^x, \Delta\right)$, then for every $A \in 2^x$; inverse of $A$ ... $\mathrm{H}$ is a group. $\mathrm{H}$ satisfies inverse prop, but not a group for every $A \in 2^x$; the inverse of $A$ is $A$.
closed
ankitgupta.1729
answered
in
Set Theory & Algebra
Feb 10
by
ankitgupta.1729
410
views
memorybased-gatecse2023
goclasses
set-theory&algebra
group-theory
multiple-selects
2
votes
1
answer
8
What is the magnitude of Adj(A) and Adj(Adj(A)) ?
What is the magnitude of Adj(A) and Adj(Adj(A)) ?
Sahil_Lather
answered
in
Set Theory & Algebra
Jan 28
by
Sahil_Lather
110
views
discrete-mathematics
1
vote
2
answers
9
Testbook set theory question for abelian group and generators
Given: Statement A: All cyclic groups are an abelian group. Statement B: The order of the cyclic group is the same as the order of its generator. 1 A and B are false 2 A is true, B is false 3 B is true, A is false 4 A and B both are true
Sahil_Lather
answered
in
Set Theory & Algebra
Jan 27
by
Sahil_Lather
75
views
set-theory&algebra
abelian-group
0
votes
1
answer
10
Testbook poset question
Which of the following is/are correct about the number of edges and number of vertices respectively in the Hasse diagram of POSET [P(A); ⊆] where P(A) is the power set and A = {a , b , c} ? 1 number of vertices = 12 2 number of vertices = 8 3 number of edges = 12 4 number of edges = 8
Sahil_Lather
answered
in
Set Theory & Algebra
Jan 27
by
Sahil_Lather
100
views
set-theory&algebra
boolean-algebra
testbook-test-series
0
votes
0
answers
11
TestBook Lattice question
Consider the relation R = {(p, p), (p, q), (p, r), (p, s), (p, t), (q, q,) (q, s), (q, t), (s, s), (s, t), (r, r), (r, t), (t ,t) which is a subset of A × A where A = {p, q, r, s, t} then which of the following is/are true? 1 (A, R) is a Boolean Algebra 2 (A, R) is a complemented lattice 3 (A, R) is distributed lattice 4 (A, R) is not a lattice
Sahil_Lather
asked
in
Set Theory & Algebra
Jan 27
by
Sahil_Lather
56
views
set-theory&algebra
boolean-algebra
lattice
1
vote
2
answers
12
Testbook group theory question
Let G be a group of order 49. Then G is abelian G is cyclic G is non-abelian Centre of G has order 7
Sahil_Lather
answered
in
Set Theory & Algebra
Jan 27
by
Sahil_Lather
83
views
set-theory&algebra
abelian-group
testbook-test-series
0
votes
1
answer
13
Kenneth Rosen Edition 7 Exercise 2.4 Question 9 (Page No. 168)
Find the first five terms of the sequence defined by each of these recurrence relations and initial conditions. $a_{n} = 6a_{n−1}, a_{0} = 2$ $a_{n} = a_{n−1}^{2}, a_{1} = 2$ $a_{n} = a_{n−1} + 3a_{n−2}, a_{0} = 1, a_{1} = 2$ ... $a_{n} = a_{n−1} + a_{n−3}, a_{0} = 1, a_{1} = 2, a_{2} = 0$
wajid rehman
answered
in
Set Theory & Algebra
Jan 20
by
wajid rehman
211
views
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
0
votes
0
answers
14
set, relation
Consider the partition of a set having 3 block of 5 elements each, 4 block of 2 elements each and 2 block of 3 elements in each block. Find the cardinality of equivalence relation.
someshawasthi
asked
in
Set Theory & Algebra
Jan 17
by
someshawasthi
80
views
discrete-mathematics
set-theory
1
vote
1
answer
15
Set theory
Let A = set of all real numbers. '*' be a binary operation a*b = a + b + a. b (A, *) is a group or not. Doubt : Till finding identity element (=0) every thing is okay. While finding inverse: a * $a^{-1}$ = e a + $a^{-1}$ + a$a^{-1}$ = 0 a + $a^{-1}$ + 1 = 0 Or a + $a^{-1}$(1+a) = 0 Both will lead to different answer. What is correct.
Johnny1001
answered
in
Set Theory & Algebra
Jan 16
by
Johnny1001
147
views
self-doubt
set-theory
21
votes
2
answers
16
GATE CSE 1987 | Question: 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?
Johnny1001
answered
in
Set Theory & Algebra
Jan 16
by
Johnny1001
2.2k
views
gate1987
set-theory&algebra
relations
descriptive
2
votes
1
answer
17
Kenneth Rosen Edition 7 Exercise 1.2 Question 18 (Page No. 23)
When planning a party you want to know whom to invite. Among the people you would like to invite are three touchy friends.You know that if Jasmine attends, she will become unhappy if Samir is there, Samir will attend only if Kanti ... logical equivalent statments. j-> not s s->k not j -> not k How to approach this question?
pavan singh
answered
in
Set Theory & Algebra
Jan 5
by
pavan singh
558
views
kenneth-rosen
discrete-mathematics
mathematical-logic
0
votes
1
answer
18
Set Theory, Basic | Power of a set
Given set A= {a,b}$^3$ What do the formed set look like and what is |A| (cardinility of A)
deepak_7891
answered
in
Set Theory & Algebra
Jan 5
by
deepak_7891
130
views
discrete-mathematics
set-theory
self-doubt
0
votes
0
answers
19
Set Theory Test Series Question
Statement 1: If $A\subseteq B$ and $B \subseteq A$ then $A= B$ Statement 2: If $A= B$ then $A\subseteq B$ or $B \subseteq A$ Which of these statements are true? Statement 1 is standard definition of Equivalence of 2 sets, so always true. Statement 2 seems to be true but I am not sure.
Sunnidhya Roy
asked
in
Set Theory & Algebra
Jan 4
by
Sunnidhya Roy
117
views
set-theory&algebra
discrete-mathematics
0
votes
1
answer
20
#gateappliedcourse
Let A={x,y,z}. The number of relations containing (x,y) and (x,z) which are reflexive and symmetric but not transitive is?
Abhrajyoti00
answered
in
Set Theory & Algebra
Jan 3
by
Abhrajyoti00
129
views
set-theory&algebra
relations
functions
1
vote
1
answer
21
Unacademy All India Mock 18 Dec. 2022.Counting
Let S={0,1,2,3,….,9}. The number of subsets of 5 contains at least two even numbers? HELP ANYONE Ans.-832
Shoto
answered
in
Set Theory & Algebra
Dec 19, 2022
by
Shoto
294
views
set-theory&algebra
counting
functions
1
vote
2
answers
22
#Unacademy
Find inverse in a*b=a+b-ab for all a,b belongs to Q-{-1}. where Q is a rational number? please explain how the inverse will satisfy the equation of inverse(a*b=b*a=e)
RinkeshP
answered
in
Set Theory & Algebra
Dec 16, 2022
by
RinkeshP
158
views
set-theory&algebra
relations
functions
binary-operation
0
votes
2
answers
23
Set Theory
We have a set of cardinality 7. Suppose P is the power set of S. We have a subset of Power set, Ps such that every pair of elements (a, b) in subset is such that, either a is a subset of b or b is a subset of a. What could be the max cardinality of Ps?
RinkeshP
answered
in
Set Theory & Algebra
Dec 16, 2022
by
RinkeshP
152
views
set-theory
set-theory
1
vote
0
answers
24
DRDO CSE 2022 Paper 1 | Question: 8
Given a powerset $S$ of $\{1,2,3\}$, its partial order $\leq$ is given by set inclusion. That is, for any subsets $T_{1} \neq T_{2}$ of $\{1,2,3\}$ we have $T_{1} \leq T_{2}$ if and only if $T_{1} \subset T_{2}$. Construct the Hasse diagram on $S$ under this partial order definition.
admin
asked
in
Set Theory & Algebra
Dec 15, 2022
by
admin
60
views
drdocse-2022-paper1
set-theory&algebra
partial-order
4-marks
descriptive
1
vote
0
answers
25
DRDO CSE 2022 Paper 1 | Question: 17
Total number of functions from set $B$ to set $A$ with $n$ and $m$ elements, respectively are ___________.
admin
asked
in
Set Theory & Algebra
Dec 15, 2022
by
admin
51
views
drdocse-2022-paper1
set-theory&algebra
functions
3-marks
fill-in-the-blanks
1
vote
0
answers
26
DRDO CSE 2022 Paper 1 | Question: 20
A partially ordered set $S=(\{3,4,12,24,48,72\}, /)$ is a _________ with _________ cycle$(s).$
admin
asked
in
Set Theory & Algebra
Dec 15, 2022
by
admin
65
views
drdocse-2022-paper1
set-theory&algebra
partial-order
4-marks
fill-in-the-blanks
31
votes
7
answers
27
GATE IT 2007 | Question: 23
A partial order $P$ is defined on the set of natural numbers as follows. Here $\frac{x}{y}$ denotes integer division. $(0, 0) \in P.$ $(a, b) \in P$ if and only if $(a \% 10) \leq (b \% 10$) and $(\frac{a}{10},\frac{b}{10})\in P.$ ... $P$? (i) and (iii) (ii) and (iv) (i) and (iv) (iii) and (iv)
iamsubhrajit
answered
in
Set Theory & Algebra
Dec 15, 2022
by
iamsubhrajit
9.1k
views
gateit-2007
set-theory&algebra
partial-order
normal
70
votes
8
answers
28
GATE CSE 2006 | Question: 25
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: $3m$ $3n$ $2m+1$ $2n+1$
sat0503
answered
in
Set Theory & Algebra
Nov 21, 2022
by
sat0503
8.4k
views
gatecse-2006
set-theory&algebra
normal
functions
1
vote
1
answer
29
KSET 2015 computer science
Let X and Y be two sets having n elements each. Then the total number of bijective functions from X and Y is (A) n (B) 2n (C) n! (D) 2n
Rekhashri
asked
in
Set Theory & Algebra
Nov 19, 2022
by
Rekhashri
135
views
set-theory&algebra
functions
0
votes
1
answer
30
Can a uniquely complemented lattice may not be distributive?
lijo
asked
in
Set Theory & Algebra
Nov 6, 2022
by
lijo
91
views
lattice
0
votes
0
answers
31
#Unacademy
**Every group of prime order is always an abelian group on this fact please explain how can a 2 element group be an abelian group, please give an example
Dknights
asked
in
Set Theory & Algebra
Nov 4, 2022
by
Dknights
143
views
set-theory&algebra
abelian-group
group-theory
1
vote
0
answers
32
Set Theory
If A = {1, 3,5,7,.......} Then (A, +) is semi group or not. Doubt : a +(b+c) =( a + b) +c So associativity property is present But a + b doesn't belong to A So closure property is not present. So A is semi group or not.
Overflow04
asked
in
Set Theory & Algebra
Oct 25, 2022
by
Overflow04
119
views
self-doubt
group-theory
set-theory
0
votes
0
answers
33
Topic: Combining relations (Composition of relations)
Let R be a relation. Why $R^2 oR^2 !=R^4$ while $R^3 oR =R^4$? Please explain.
Yamini_learner
asked
in
Set Theory & Algebra
Sep 26, 2022
by
Yamini_learner
115
views
relations
1
vote
2
answers
34
KENNITH ROSEN LATTICE
Find a compatible total order for the divisibility relation on the set {1, 2, 3, 6, 8, 12, 24, 36}.
shreyo
asked
in
Set Theory & Algebra
Sep 26, 2022
by
shreyo
215
views
discrete-mathematics
kenneth-rosen
lattice
0
votes
1
answer
35
Gate At Zeal
Question → If (G,*) is a group of order 960 and there exist a in G such that a^m=e for some integer m<=960 where e is identity element of G then total number of possible value of m is___________ Answer==28
lalitver10
asked
in
Set Theory & Algebra
Sep 17, 2022
by
lalitver10
231
views
group-theory
discrete-mathematics
test-series
zeal
0
votes
1
answer
36
TIFR CSE 2022 | Part A | Question: 9
You are given the following properties of sets $A, B, X$, and $Y$. For notation, $|A|$ denotes the cardinality of set $A$ (i.e., the number of elements in $A$ ), and $A \backslash B$ denotes the set of elements that are in $A$ but not in $B$. $A \cup B=X \cup Y$ ... $|X|=5$ $|Y|=5$ $|A \cup X|=|B \cup Y|$ $|A \cap X|=|B \cap Y|$ $|A|=|B|$
Lakshman Patel RJIT
asked
in
Set Theory & Algebra
Sep 1, 2022
by
Lakshman Patel RJIT
144
views
tifr2022
set-theory&algebra
set-theory
0
votes
0
answers
37
TIFR CSE 2022 | Part A | Question: 11
Let $X$ be a finite set. A family $\mathcal{F}$ of subsets of $X$ is said to be upward closed if the following holds for all sets $A, B \subseteq X$ ... $\mathcal{F} \sqcup \mathcal{G}=\mathcal{G} \backslash \mathcal{F}$ None of the above
Lakshman Patel RJIT
asked
in
Set Theory & Algebra
Sep 1, 2022
by
Lakshman Patel RJIT
88
views
tifr2022
set-theory&algebra
set-theory
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Recent questions and answers in Set Theory & Algebra
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Please upload updated previous year question...
The last hardcopy that was made was for GATE 2022...
overall only 3 post .no post for gen male
for gen GS in the range of 720-750 approx.
can we get 2023 hark copy from amazon?