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Recent questions tagged set-theory&algebra

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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.

admin asked in Set Theory & Algebra Feb 15

by admin

876 views

1 vote

1 answer

2

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 $A$.

admin asked in Set Theory & Algebra Feb 15

by admin

1.0k views

1 vote

2 answers

3

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 $A$.

GO Classes asked in Set Theory & Algebra Feb 6

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0 votes

1 answer

4

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 asked in Set Theory & Algebra Jan 27

by Sahil_Lather

96 views

0 votes

0 answers

5

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

55 views

1 vote

2 answers

6

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 asked in Set Theory & Algebra Jan 27

by Sahil_Lather

68 views

1 vote

2 answers

7

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 asked in Set Theory & Algebra Jan 27

by Sahil_Lather

81 views

0 votes

0 answers

8

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

113 views

0 votes

1 answer

9

#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?

Dknights asked in Set Theory & Algebra Jan 2

127 views

1 vote

1 answer

10

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

Rajender gill asked in Set Theory & Algebra Dec 19, 2022

by Rajender gill

292 views

1 vote

0 answers

11

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

58 views

1 vote

0 answers

12

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

49 views

1 vote

0 answers

13

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

62 views

1 vote

1 answer

14

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

128 views

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Recent questions tagged set-theory&algebra