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Recent questions tagged set-theory&algebra
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GATE CSE 2024 | Set 2 | Question: 24
Let $\text{P}$ be the partial order defined on the set $\{1,2,3,4\}$ as follows \[ P=\{(x, x) \mid x \in\{1,2,3,4\}\} \cup\{(1,2),(3,2),(3,4)\} \] The number of total orders on $\{1,2,3,4\}$ that contain $\text{P}$ is __________.
Arjun
asked
in
Set Theory & Algebra
Feb 16
by
Arjun
1.7k
views
gatecse2024-set2
numerical-answers
set-theory&algebra
partial-order
2
votes
2
answers
2
GATE CSE 2024 | Set 2 | Question: 53
Let $Z_{n}$ be the group of integers $\{0,1,2, \ldots, n-1\}$ with addition modulo $n$ as the group operation. The number of elements in the group $Z_{2} \times Z_{3} \times Z_{4}$ that are their own inverses is ___________.
Arjun
asked
in
Set Theory & Algebra
Feb 16
by
Arjun
1.7k
views
gatecse2024-set2
numerical-answers
set-theory&algebra
group-theory
0
votes
1
answer
3
GATE CSE 2024 | Set 1 | Question: 22
Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions $\text{(i)}$ from $A$ to $B$ and $\text{(ii)}$ from $A \times A$ to $A \cup B$. The number of possible values of $\text{|A|}$ is ___________.
Arjun
asked
in
Set Theory & Algebra
Feb 16
by
Arjun
1.5k
views
gatecse2024-set1
numerical-answers
set-theory&algebra
1
vote
1
answer
4
GATE CSE 2024 | Set 1 | Question: 42
Consider the operators $\diamond$ and $\square$ defined by $a \diamond b=a+2 b, a \square b=a b$, for positive integers. Which of the following statements is/are TRUE? Operator $\diamond$ ... $\square$ obeys the distributive law Operator $\square$ over the operator $\diamond$ obeys the distributive law
Arjun
asked
in
Set Theory & Algebra
Feb 16
by
Arjun
1.6k
views
gatecse2024-set1
multiple-selects
set-theory&algebra
3
votes
1
answer
5
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 39
For sets $A$ and $B$, let $f: A \rightarrow B$ and $g: B \rightarrow A$ be functions such that $f(g(x))=x$ for each $x \in B$. Which among the following statements is/are correct? The function $f$ must be one-to-one. The function $f$ must be onto. The function g must be one-to-one. The function $g$ must be onto.
GO Classes
asked
in
Set Theory & Algebra
Feb 5
by
GO Classes
438
views
goclasses2024-mockgate-14
set-theory&algebra
functions
multiple-selects
2-marks
3
votes
1
answer
6
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 28
A group $G$ in which $(a b)^2=a^2 b^2$ for all $a, b$ in $G$ is necessarily finite cyclic abelian none of the above
GO Classes
asked
in
Set Theory & Algebra
Jan 28
by
GO Classes
303
views
goclasses2024-mockgate-13
goclasses
set-theory&algebra
group-theory
1-mark
3
votes
0
answers
7
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 61
Let $S$ be the set of all functions $f: \mathbb{R} \rightarrow \mathbb{R}$. Consider the two binary operations + and $\circ$ on $S$ ... law $(g+h) \circ f=(g \circ f)+(h \circ f)$. None III only II and III only I, II, and III
GO Classes
asked
in
Set Theory & Algebra
Jan 28
by
GO Classes
399
views
goclasses2024-mockgate-13
goclasses
set-theory&algebra
group-theory
2-marks
4
votes
1
answer
8
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 62
As a refresher, if $R$ is an equivalence relation over a set $A$ and $x \in A$, then the equivalence class of $\boldsymbol{x}$ in $\boldsymbol{R}$, denoted $[x]_R,$ is the set $ [x]_R=\{y \in A \mid x R y\} $ Let's now introduce some ... $\mathrm{I}(\mathrm{R})=n / 2$ and $\mathrm{W}(\mathrm{R})=n / 2$
GO Classes
asked
in
Set Theory & Algebra
Jan 28
by
GO Classes
451
views
goclasses2024-mockgate-13
goclasses
set-theory&algebra
set-theory
relations
equivalence-class
2-marks
2
votes
1
answer
9
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 19
Let $\ast $ be the binary operation on the rational numbers given by $a \ast b=a+b+2 a b$. Which of the following are true? $\ast $ is commutative There is a rational number that is a $\ast \;-$ identity. Every rational number has a $\ast \;-$ inverse. I only I and II only I and III only I, II, and III
GO Classes
asked
in
Set Theory & Algebra
Jan 21
by
GO Classes
419
views
goclasses2024-mockgate-12
goclasses
set-theory&algebra
group-theory
1-mark
6
votes
1
answer
10
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 47
An involution is a function $f: A \rightarrow A$ where $f(f(x))=x$. A fixed point of any function $f: A \rightarrow A$ is an element $x \in A$ for which $f(x)$ $=x$. Which of the following statement(s) ... $f: \mathrm{A} \rightarrow \mathrm{A}$ is a bijective function.
GO Classes
asked
in
Set Theory & Algebra
Jan 21
by
GO Classes
405
views
goclasses2024-mockgate-12
goclasses
set-theory&algebra
functions
multiple-selects
2-marks
8
votes
1
answer
11
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 12
Let $A-B$ denote $\{x \in A: x \notin B\}$. If $(A-B) \cup B=A$, which of the following must be true? $B$ is empty $A \subseteq B$ $B \subseteq A$ $(B-A) \cup A=B$
GO Classes
asked
in
Set Theory & Algebra
Jan 13
by
GO Classes
573
views
goclasses2024-mockgate-11
goclasses
set-theory&algebra
set-theory
1-mark
5
votes
1
answer
12
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 18
If $F$ is a function such that, for all positive integers $x$ and $y, F(x, 1)=x+1, F(1, y)=2 y$, and $F(x+1, y+1)=F(F(x, y+1), y)$, then $F(2,3)=$
GO Classes
asked
in
Set Theory & Algebra
Jan 13
by
GO Classes
467
views
goclasses2024-mockgate-11
goclasses
numerical-answers
set-theory&algebra
functions
1-mark
2
votes
1
answer
13
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 37
If $b$ and $c$ are elements in a group $G$, and if $b^5=c^3=e$, where $e$ is the unit element of $G$, then the inverse of $b^2 c b^4 c^2$ must be $b^4 c^2 b^2 c$ $c^2 b^4 c b^2$ $c b^2 c^2 b^4$ $c b c^2 b^3$
GO Classes
asked
in
Set Theory & Algebra
Jan 13
by
GO Classes
381
views
goclasses2024-mockgate-11
goclasses
set-theory&algebra
group-theory
2-marks
8
votes
1
answer
14
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 38
A binary relation $\mathrm{R}$ over a set $\mathrm{A}$ is called a "GO Relation" if for all $\mathrm{x}, \mathrm{y}, \mathrm{z}$ $\in A$, if $x R y$ and $x R z$, then $y R z$. Which of the following ... is transitive. If $R$ is a GO relation then $R$ is reflexive. If $R$ is an equivalence relation then $R$ is a GO relation.
GO Classes
asked
in
Set Theory & Algebra
Jan 13
by
GO Classes
502
views
goclasses2024-mockgate-11
goclasses
set-theory&algebra
relations
multiple-selects
2-marks
0
votes
0
answers
15
If G be a group and a,b in G such that a²=e and aba^-1 = b⁷ then prove that b⁴⁰= e
Anikumar
asked
in
Set Theory & Algebra
Aug 31, 2023
by
Anikumar
190
views
set-theory&algebra
0
votes
0
answers
16
De Morgan's
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Aug 28, 2023
by
Çșȇ ʛấẗẻ
87
views
set-theory&algebra
0
votes
0
answers
17
Set theory
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Aug 28, 2023
by
Çșȇ ʛấẗẻ
65
views
set-theory&algebra
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