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Recent questions and answers in Set Theory & Algebra
41
votes
9
answers
1
GATE CSE 1996 | Question: 2.1
Let $R$ denote the set of real numbers. Let $f:R\times R \rightarrow R \times R$ be a bijective function defined by $f(x,y) = (x+y, x-y)$. The inverse function of $f$ is given by $f^{-1} (x,y) = \left( \frac {1}{x+y}, \frac{1}{x-y}\right)$ ... $f^{-1}(x,y)=\left [ 2\left(x-y\right),2\left(x+y\right) \right ]$
ritiksri8
answered
in
Set Theory & Algebra
Mar 20
by
ritiksri8
9.6k
views
gate1996
set-theory&algebra
functions
normal
36
votes
6
answers
2
GATE CSE 2017 Set 2 | Question: 21
Consider the set $X=\{a, b, c, d, e\}$ under partial ordering $R=\{(a,a), (a, b), (a, c), (a, d), (a, e), (b, b), (b, c), (b, e), (c, c), (c, e), (d, d), (d, e), (e, e) \}$ The Hasse diagram of the partial order $(X, R)$ is shown below. The minimum number of ordered pairs that need to be added to $R$ to make $(X, R)$ a lattice is ______
ritiksri8
answered
in
Set Theory & Algebra
Mar 17
by
ritiksri8
11.8k
views
gatecse-2017-set2
set-theory&algebra
lattice
numerical-answers
normal
0
votes
2
answers
3
Find no of sets A and B such that A n B = {3,5} and A U B = {2,3,5,7,8)
I_M_CK
answered
in
Set Theory & Algebra
Mar 13
by
I_M_CK
98
views
24
votes
6
answers
4
GATE CSE 1995 | Question: 1.20
The number of elements in the power set $P(S)$ of the set $S=\{\{\emptyset\}, 1, \{2, 3\}\}$ is: $2$ $4$ $8$ None of the above
ritiksri8
answered
in
Set Theory & Algebra
Mar 9
by
ritiksri8
16.2k
views
gate1995
set-theory&algebra
normal
set-theory
20
votes
5
answers
5
TIFR CSE 2016 | Part A | Question: 8
Let $A$ and $B$ be finite sets such that $A \subseteq B$. Then, what is the value of the expression: $ \sum \limits_{C:A \subseteq C \subseteq B} (-1)^{\mid C \setminus A \mid,}$ Where $C \setminus A=\{x \in C : x \notin A \}$? Always $0$ Always $1$ $0$ if $A=B$ and $1$ otherwise $1$ if $A=B$ and $0$ otherwise Depends on the size of the universe
Priyam Garg
answered
in
Set Theory & Algebra
Feb 28
by
Priyam Garg
2.7k
views
tifr2016
set-theory&algebra
set-theory
0
votes
0
answers
6
Question on Quotient set
What will be quotient set for equivalence relation R={(x,y) ∣ x ≡ y mod 5} in set builder form?
rick55
asked
in
Set Theory & Algebra
Feb 23
by
rick55
55
views
2
votes
2
answers
7
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 ___________.
amit166
answered
in
Set Theory & Algebra
Feb 22
by
amit166
1.8k
views
gatecse2024-set2
numerical-answers
set-theory&algebra
group-theory
1
vote
2
answers
8
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 __________.
amit166
answered
in
Set Theory & Algebra
Feb 22
by
amit166
1.8k
views
gatecse2024-set2
numerical-answers
set-theory&algebra
partial-order
1
vote
1
answer
9
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
shishir__roy
answered
in
Set Theory & Algebra
Feb 16
by
shishir__roy
1.6k
views
gatecse2024-set1
multiple-selects
set-theory&algebra
0
votes
1
answer
10
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 ___________.
shishir__roy
answered
in
Set Theory & Algebra
Feb 16
by
shishir__roy
1.6k
views
gatecse2024-set1
numerical-answers
set-theory&algebra
24
votes
4
answers
11
GATE CSE 1987 | Question: 9a
How many binary relations are there on a set $A$ with $n$ elements?
ssingla
answered
in
Set Theory & Algebra
Feb 7
by
ssingla
5.8k
views
gate1987
set-theory&algebra
relations
descriptive
0
votes
0
answers
12
#self doubt
Can someone please verify it ? isn't should be 8. https://www.toppr.com/ask/question/the-cardinality-of-the-power-set-of-left-phi-left-phiright-left-phi-left/ Let S={ϕ,{ϕ},{ϕ,{ϕ}}} P(s)= Power Set of set S P(s)={ϕ,{ϕ},{ϕ,{ϕ}},{ϕ,{ϕ,{ϕ}}},{{ϕ},{ϕ,{ϕ}}},{ϕ,{ϕ},{ϕ,{ϕ}}}} n(P(s))=6.
Dknights
asked
in
Set Theory & Algebra
Feb 6
by
Dknights
111
views
discrete-mathematics
3
votes
1
answer
13
TIFR-2015-Maths-A-15
The series $\sum_{n=1}^{\infty}\frac{\cos (3^{n}x)}{2^{n}}$ Diverges, for all rational $x \in \mathbb{R}$ Diverges, for some irrational $x \in \mathbb{R}$ Converges, for some but not all $x \in \mathbb{R}$ Converges, for all $x \in \mathbb{R}$
Lakshmi Narayana404
answered
in
Set Theory & Algebra
Feb 6
by
Lakshmi Narayana404
335
views
tifrmaths2015
convergence
non-gate
25
votes
9
answers
14
GATE CSE 2017 Set 1 | Question: 47
The number of integers between $1$ and $500$ (both inclusive) that are divisible by $3$ or $5$ or $7$ is ____________ .
Kimo123
answered
in
Set Theory & Algebra
Feb 5
by
Kimo123
11.6k
views
gatecse-2017-set1
set-theory&algebra
normal
numerical-answers
set-theory
3
votes
1
answer
15
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
answered
in
Set Theory & Algebra
Feb 5
by
GO Classes
463
views
goclasses2024-mockgate-14
set-theory&algebra
functions
multiple-selects
2-marks
4
votes
1
answer
16
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 $\mathrm{W}(\mathrm{R})=n / 2$
Deepak Poonia
answered
in
Set Theory & Algebra
Jan 29
by
Deepak Poonia
464
views
goclasses2024-mockgate-13
goclasses
set-theory&algebra
set-theory
relations
equivalence-class
2-marks
0
votes
1
answer
17
Made easy mock test questions from Functions
Can you explain the procedure and if possible can you share some links to any youtube playlist from where I can study this particular subject(Functions).
ByteCode
answered
in
Set Theory & Algebra
Jan 28
by
ByteCode
147
views
test-series
functions
discrete-mathematics
gate-preparation
made-easy-test-series
3
votes
1
answer
18
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
answered
in
Set Theory & Algebra
Jan 28
by
GO Classes
317
views
goclasses2024-mockgate-13
goclasses
set-theory&algebra
group-theory
1-mark
3
votes
0
answers
19
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
408
views
goclasses2024-mockgate-13
goclasses
set-theory&algebra
group-theory
2-marks
2
votes
1
answer
20
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
answered
in
Set Theory & Algebra
Jan 21
by
GO Classes
443
views
goclasses2024-mockgate-12
goclasses
set-theory&algebra
group-theory
1-mark
6
votes
1
answer
21
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
answered
in
Set Theory & Algebra
Jan 21
by
GO Classes
417
views
goclasses2024-mockgate-12
goclasses
set-theory&algebra
functions
multiple-selects
2-marks
8
votes
1
answer
22
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
answered
in
Set Theory & Algebra
Jan 13
by
GO Classes
626
views
goclasses2024-mockgate-11
goclasses
set-theory&algebra
set-theory
1-mark
5
votes
1
answer
23
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
answered
in
Set Theory & Algebra
Jan 13
by
GO Classes
490
views
goclasses2024-mockgate-11
goclasses
numerical-answers
set-theory&algebra
functions
1-mark
2
votes
1
answer
24
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
answered
in
Set Theory & Algebra
Jan 13
by
GO Classes
401
views
goclasses2024-mockgate-11
goclasses
set-theory&algebra
group-theory
2-marks
8
votes
1
answer
25
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
answered
in
Set Theory & Algebra
Jan 13
by
GO Classes
550
views
goclasses2024-mockgate-11
goclasses
set-theory&algebra
relations
multiple-selects
2-marks
0
votes
1
answer
26
GATE 2018 | MATHS | Q-40
Which one of the following statements is true? (A) Every group of order 12 has a non-trivial proper normal subgroup (B) Some group of order 12 does not have a non-trivial proper normal subgroup (C) Every group of order 12 has a subgroup of order 6 (D) Every group of order 12 has an element of order 12
rajveer43
answered
in
Set Theory & Algebra
Jan 11
by
rajveer43
111
views
set-theory
1
vote
0
answers
27
GATE 2019 | maths | set theory
Consider the following statements: I.The set $ \mathbb{R} $ is uncountable. II.The set $ \{ f : f \text{ is a function from } \mathbb{N} \text{ to } \{0, 1\} \} $ is uncountable. III.The set $ \{ p : p \text{ is a prime number} \} $ is uncountable. ... of the above statements are TRUE? (A)] I and IV only (B) II and IV only (C) II and III only (D) I, II, and IV only
rajveer43
asked
in
Set Theory & Algebra
Jan 10
by
rajveer43
67
views
set-theory
0
votes
0
answers
28
GATE 2021 | MATHS | Q-20
Let $ f: \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) \to \mathbb{R} $ be given by $ f(x) = \frac{\pi}{2} + x - \tan^{-1}(x) $. Consider the following statements: $P:$ $ |f(x) - f(y)| < |x - y| $ ... Then the correct option is: (A) both P and Q are TRUE (B) P is TRUE and Q is FALSE (C) P is FALSE and Q is TRUE (D) both P and Q are FALSE
rajveer43
asked
in
Set Theory & Algebra
Jan 10
by
rajveer43
55
views
functions
set-theory
0
votes
0
answers
29
GATE 2022 | MATHS | Q-27
The number of subgroups of a cyclic group of order 12 is ______________________
rajveer43
asked
in
Set Theory & Algebra
Jan 10
by
rajveer43
50
views
discrete-mathematics
0
votes
1
answer
30
GATE 2023 | Maths | Sample Ques for CS-IT
Let \(G\) be an abelian group and \(\Phi: G \rightarrow (\mathbb{Z}, +)\) be a surjective group homomorphism. Let \(1 = \Phi(a)\) for some \(a \in G\). Consider the following statements: \(P\): For every \(g \in G\), there exists an \(n \in \ ... following statements is/are correct? (A) \(P\) is TRUE (B) \(P\) is FALSE (C) \(Q\) is TRUE (D) \(Q\) is FALSE
rajveer43
answered
in
Set Theory & Algebra
Jan 10
by
rajveer43
69
views
set-theory
discrete-mathematics
2
votes
1
answer
31
TIFR-2015-Maths-A-11
Let $\left\{a_{n}\right\}$ be a sequence of real numbers. Which of the following is true? If $\sum a_{n}$ converges, then so does $\sum a_{n}^{4}$ If $\sum |a_{n}|$ converges, then so does $\sum a_{n}^{2}$ If $\sum a_{n}$ diverges, then so does $\sum a_{n}^{3}$ If $\sum |a_{n}|$ diverges, then so does $\sum a_{n}^{2}$
Lakshmi Narayana404
answered
in
Set Theory & Algebra
Jan 8
by
Lakshmi Narayana404
356
views
tifrmaths2015
convergence
non-gate
78
votes
6
answers
32
GATE CSE 2014 Set 3 | Question: 49
Consider the set of all functions $f:\{0,1, \dots,2014\} \to \{0,1,\dots, 2014\}$ such that $ f\left(f\left(i\right)\right)=i$, for all $0 \leq i \leq 2014$. Consider the following statements: $P$. For each such function it must be the case that for every ... is CORRECT? $P, Q$ and $R$ are true Only $Q$ and $R$ are true Only $P$ and $Q$ are true Only $R$ is true
Deepak Poonia
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Set Theory & Algebra
Jan 5
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Deepak Poonia
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gatecse-2014-set3
set-theory&algebra
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0
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1
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33
MADE EASY TEST SERIES
Pls solve it
aie0063
answered
in
Set Theory & Algebra
Jan 4
by
aie0063
181
views
discrete-mathematics
made-easy-test-series
51
votes
15
answers
34
GATE CSE 2015 Set 2 | Question: 40
The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.
vinayedula
answered
in
Set Theory & Algebra
Dec 29, 2023
by
vinayedula
19.3k
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gatecse-2015-set2
set-theory&algebra
functions
normal
numerical-answers
43
votes
2
answers
35
GATE CSE 1989 | Question: 1-v
The number of possible commutative binary operations that can be defined on a set of $n$ elements (for a given $n$) is ___________.
anujs
answered
in
Set Theory & Algebra
Dec 27, 2023
by
anujs
6.5k
views
gate1989
descriptive
set-theory&algebra
binary-operation
0
votes
0
answers
36
#self doubt
If [dn,/] is a lattice, then x=n/x for all x belongs to dn
Dknights
asked
in
Set Theory & Algebra
Dec 21, 2023
by
Dknights
67
views
discrete-mathematics
0
votes
0
answers
37
#function#self doubt
Can someone verify the above inferences?
Dknights
asked
in
Set Theory & Algebra
Dec 10, 2023
by
Dknights
117
views
discrete-mathematics
0
votes
0
answers
38
#selfdoubt
‘either or’ can be taken as union in discrete mathematics?
Dknights
asked
in
Set Theory & Algebra
Dec 10, 2023
by
Dknights
111
views
discrete-mathematics
43
votes
5
answers
39
GATE CSE 2006 | Question: 3
The set $\{1,2,3,5,7,8,9\}$ under multiplication modulo $10$ is not a group. Given below are four possible reasons. Which one of them is false? It is not closed $2$ does not have an inverse $3$ does not have an inverse $8$ does not have an inverse
Hira Thakur
answered
in
Set Theory & Algebra
Dec 1, 2023
by
Hira Thakur
9.8k
views
gatecse-2006
set-theory&algebra
group-theory
normal
30
votes
4
answers
40
GATE CSE 1993 | Question: 28
Let $\left(\{ p,q \},*\right)$ be a semigroup where $p*p=q$. Show that: $p*q=q*p$ and $q*q=q$
Amoljadhav
answered
in
Set Theory & Algebra
Nov 30, 2023
by
Amoljadhav
4.6k
views
gate1993
set-theory&algebra
group-theory
normal
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