Recent questions tagged set-theory&algebra / GATE Overflow for GATE CSE

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121

Hasse diagram
Draw the Hasse diagram for the "divides" relation (∣) on the set {0,1,…,26}

Draw the Hasse diagram for the "divides" relation (∣) on the set {0,1,…,26}

Çșȇ ʛấẗẻ

131 views

Çșȇ ʛấẗẻ asked Apr 17, 2023

1 votes

1 answer

122

GO Classes 2023 | IIITH Mock Test 1 | Question: 1
Let $\text{R}$ be a relation from a set $\text{A}$ to a set $\text{B}.$ The inverse relation from $\text{B}$ to $\text{A},$ denoted by $\text{R}^{-1},$ is the set of ordered pairs $\{(b,a) \mid (a,b) \in R\}$ ... $\text{S1}$ Only $\text{S2}$ Both $\text{S1}$ and $\text{S2}$ None of the above

Let $\text{R}$ be a relation from a set $\text{A}$ to a set $\text{B}.$ The inverse relation from $\text{B}$ to $\text{A},$ denoted by $\text{R}^{-1},$ is the set of orde...

GO Classes

821 views

GO Classes asked Mar 26, 2023

4 votes

2 answers

123

GO Classes 2023 | IIITH Mock Test 1 | Question: 2
Given a set of values $\text{R} = \{1,2,3,4,5,6,7\}.$ The number of relations on this set which are both partial-order and equivalence relation is? $128$ $1$ $0$ $2^{42}$

Given a set of values $\text{R} = \{1,2,3,4,5,6,7\}.$ The number of relations on this set which are both partial-order and equivalence relation is?$128$$1$$0$$2^{42}$

GO Classes

888 views

GO Classes asked Mar 26, 2023

1 votes

1 answer

124

GO Classes 2023 | IIITH Mock Test 1 | Question: 5
$(\text{Q}, \ast)$ is an algebraic structure where $\text{Q}$ represents rational numbers and $\ast$ denotes multiplication. Which one of the following statements is true? $\text{Q}$ is an abelian group. $\text{Q}$ is a group but not abelian. $\text{Q}$ is a semigroup but not a monoid. $\text{Q}$ is monoid but not group.

$(\text{Q}, \ast)$ is an algebraic structure where $\text{Q}$ represents rational numbers and $\ast$ denotes multiplication. Which one of the following statements is true...

GO Classes

707 views

GO Classes asked Mar 26, 2023

3 votes

1 answer

125

TIFR CSE 2023 | Part B | Question: 4
Amar, Balu, and Chhaya are three friends and they play the following game. Chhaya first chooses a number $k \in U$ where $U=\{1,2, \ldots, 127\}$. She either gives $k$ to both Amar and Balu, or else she gives $k$ to Amar and $k+1$ to Balu ... differed by $1.$ What is the minimal $n$ that allows Balu to distinguish between these two cases? $1$ $2$ $7$ $127$ $128$

Amar, Balu, and Chhaya are three friends and they play the following game. Chhaya first chooses a number $k \in U$ where $U=\{1,2, \ldots, 127\}$. She either gives $k$ to...

admin

399 views

admin asked Mar 14, 2023

5 votes

1 answer

126

TIFR CSE 2023 | Part A | Question: 4
Let $\mathbb{R}$ be the set of all real numbers. Consider the relation $T$ defined as \[ T=\{(x, y) \in \mathbb{R} \times \mathbb{R} \text { such that } 4+x y>0\} \] $($Recall that ... but not symmetric an equivalence relation reflexive and symmetric but not transitive symmetric but not reflexive and not transitive symmetric and transitive but not reflexive

Let $\mathbb{R}$ be the set of all real numbers. Consider the relation $T$ defined as\[T=\{(x, y) \in \mathbb{R} \times \mathbb{R} \text { such that } 4+x y>0\}\]$($Recal...

admin

429 views

admin asked Mar 14, 2023

3 votes

1 answer

127

TIFR CSE 2023 | Part A | Question: 10
Let $Q$ be a set with $n$ elements. Consider a system with states of the form $(S, R)$ where $S \subseteq Q$ and $R \subseteq Q$, with the further restriction that $R \subseteq S$. Note that $(\emptyset, \emptyset)$ is also a valid state of the system (here $\emptyset$ ... have? $3^{n}$ $2^{n}$ $4^{n}$ $n^{3}$ $\left(\begin{array}{l}n \\ 3\end{array}\right)$

Let $Q$ be a set with $n$ elements. Consider a system with states of the form $(S, R)$ where $S \subseteq Q$ and $R \subseteq Q$, with the further restriction that $R \su...

admin

376 views

admin asked Mar 14, 2023

3 votes

1 answer

128

TIFR CSE 2023 | Part A | Question: 11
We are given a set $S=\left\{x_{1}, \ldots, x_{n}\right\}$ of distinct positive integers such that $\operatorname{gcd}\left(x_{i}, x_{j}\right)= 1$ for any $i, j \in\{1, \ldots, n\}$ where $i \neq j$. What is the total number of invertible $2 \times 2$ matrices whose entries are ... $n^{2}(n-1)^{2} / 4$ $n(n-1)(n-2)(n-3)$ $n(n-1)(n-2)(n-3) / 4$ !

We are given a set $S=\left\{x_{1}, \ldots, x_{n}\right\}$ of distinct positive integers such that $\operatorname{gcd}\left(x_{i}, x_{j}\right)= 1$ for any $i, j \in\{1, ...

admin

320 views

admin asked Mar 14, 2023

14 votes

3 answers

129

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.

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_{...

admin

5.9k views

admin asked Feb 15, 2023

10 votes

2 answers

130

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 $A$.

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^{...

admin

5.7k views

admin asked Feb 15, 2023

1 votes

2 answers

131

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 $A$.

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\r...

GO Classes

899 views

GO Classes asked Feb 5, 2023

0 votes

1 answer

132

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

Which of the following is/are correct about the number of edges and number of vertices respectively in the Hasse diagram ofPOSET [P(A); ⊆] where P(A) is the power set a...

Sahil_Lather

524 views

Sahil_Lather asked Jan 27, 2023

0 votes

0 answers

133

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

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 = {...

Sahil_Lather

404 views

Sahil_Lather asked Jan 27, 2023

1 votes

2 answers

134

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

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.1A and B are false2A is tru...

Sahil_Lather

511 views

Sahil_Lather asked Jan 27, 2023

1 votes

2 answers

135

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

Let G be a group of order 49. ThenG is abelianG is cyclicG is non-abelianCentre of G has order 7

Sahil_Lather

533 views

Sahil_Lather asked Jan 27, 2023

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