Dark Mode

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

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

7.9k views

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

108 views

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

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

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

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

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

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

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

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

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

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

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

147 views

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

2.2k views

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

558 views

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

130 views

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

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

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

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

158 views

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

152 views

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

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

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

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

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

8.4k views

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

135 views

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

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

143 views

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

119 views

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

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

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

231 views

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

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

Help get things started by asking a question.

Recent questions and answers in Set Theory & Algebra