Search results for set-theory / GATE Overflow for GATE CSE

34 votes

6 answers

1

GATE CSE 1996 | Question: 1.4
Which of the following statements is FALSE? The set of rational numbers is an abelian group under addition The set of integers in an abelian group under addition The set of rational numbers form an abelian group under multiplication The set of real numbers excluding zero is an abelian group under multiplication

Which of the following statements is FALSE?The set of rational numbers is an abelian group under additionThe set of integers in an abelian group under additionThe set of ...

Kathleen

23.0k views

Kathleen asked Oct 9, 2014

85 votes

8 answers

2

GATE CSE 2016 Set 2 | Question: 28
Consider a set $U$ of $23$ different compounds in a chemistry lab. There is a subset $S$ of $U$ of $9$ compounds, each of which reacts with exactly $3$ compounds of $U$. Consider the following statements: Each compound in U \ S reacts ... \ S reacts with an even number of compounds. Which one of the above statements is ALWAYS TRUE? Only I Only II Only III None.

Consider a set $U$ of $23$ different compounds in a chemistry lab. There is a subset $S$ of $U$ of $9$ compounds, each of which reacts with exactly $3$ compounds of $U$. ...

Akash Kanase

16.6k views

Akash Kanase asked Feb 12, 2016

66 votes

6 answers

3

GATE CSE 2015 Set 1 | Question: 1‏6
For a set $A$, the power set of $A$ is denoted by $2^{A}$. If $A = \left\{5,\left\{6\right\}, \left\{7\right\}\right\}$, which of the following options are TRUE? $\varnothing \in 2^{A}$ $\varnothing \subseteq 2^{A}$ ... I and III only II and III only I, II and III only I, II and IV only

For a set $A$, the power set of $A$ is denoted by $2^{A}$. If $A = \left\{5,\left\{6\right\}, \left\{7\right\}\right\}$, which of the following options are TRUE?$\varnoth...

makhdoom ghaya

15.5k views

makhdoom ghaya asked Feb 13, 2015

77 votes

8 answers

4

GATE CSE 2014 Set 2 | Question: 50
Consider the following relation on subsets of the set $S$ of integers between $1$ and $2014$. For two distinct subsets $U$ and $V$ of $S$ we say $U\:<\:V$ if the minimum element in the symmetric difference of the two sets is in $U$. Consider the ... $S1$ is true and $S2$ is false $S2$ is true and $S1$ is false Neither $S1$ nor $S2$ is true

Consider the following relation on subsets of the set $S$ of integers between $1$ and $2014$. For two distinct subsets $U$ and $V$ of $S$ we say $U\:<\:V$ if the minimum ...

go_editor

15.9k views

go_editor asked Sep 28, 2014

24 votes

6 answers

5

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

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

Kathleen

16.3k views

Kathleen asked Oct 8, 2014

77 votes

6 answers

6

GATE CSE 2014 Set 3 | Question: 50
There are two elements $x,\:y$ in a group $(G,*)$ such that every element in the group can be written as a product of some number of $x$'s and $y$'s in some order. It is known that $x*x=y*y=x*y*x*y=y*x*y*x=e$ where $e$ is the identity element. The maximum number of elements in such a group is ____.

There are two elements $x,\:y$ in a group $(G,*)$ such that every element in the group can be written as a product of some number of $x$'s and $y$'s in some order. It is ...

go_editor

15.6k views

go_editor asked Sep 28, 2014

35 votes

4 answers

7

GATE CSE 2019 | Question: 34
Consider the following sets: S1: Set of all recursively enumerable languages over the alphabet $\{0, 1\}$ S2: Set of all syntactically valid C programs S3: Set of all languages over the alphabet $\{0,1\}$ S4: Set of all non-regular languages over the alphabet $\{ 0,1 \}$ Which of the above sets are uncountable? S1 and S2 S3 and S4 S2 and S3 S1 and S4

Consider the following sets:S1: Set of all recursively enumerable languages over the alphabet $\{0, 1\}$S2: Set of all syntactically valid C programsS3: Set of all langua...

Arjun

13.1k views

Arjun asked Feb 7, 2019

60 votes

6 answers

8

GATE CSE 2000 | Question: 2.6
Let $P(S)$ denotes the power set of set $S.$ Which of the following is always true? $P(P(S)) = P(S)$ $P(S) ∩ P(P(S)) = \{ Ø \}$ $P(S) ∩ S = P(S)$ $S ∉ P(S)$

Let $P(S)$ denotes the power set of set $S.$ Which of the following is always true?$P(P(S)) = P(S)$$P(S) ∩ P(P(S)) = \{ Ø \}$$P(S) ∩ S = P(S)$$S ∉ P(S)$

Kathleen

13.5k views

Kathleen asked Sep 14, 2014

25 votes

9 answers

9

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 ____________ .

The number of integers between $1$ and $500$ (both inclusive) that are divisible by $3$ or $5$ or $7$ is ____________ .

Arjun

11.7k views

Arjun asked Feb 14, 2017

38 votes

9 answers

10

GATE CSE 2019 | Question: 10
Let $G$ be an arbitrary group. Consider the following relations on $G$: $R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a = g^{-1}bg$ ... $R_1$ and $R_2$ $R_1$ only $R_2$ only Neither $R_1$ nor $R_2$

Let $G$ be an arbitrary group. Consider the following relations on $G$:$R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a ...

Arjun

17.4k views

Arjun asked Feb 7, 2019

45 votes

10 answers

11

GATE IT 2005 | Question: 33
Let $A$ be a set with $n$ elements. Let $C$ be a collection of distinct subsets of $A$ such that for any two subsets $S_1$ and $S_2$ in $C$, either $S_1 \subset S_2$ or $S_2\subset S_1$. What is the maximum cardinality of $C?$ $n$ $n+1$ $2^{n-1} + 1$ $n!$

Let $A$ be a set with $n$ elements. Let $C$ be a collection of distinct subsets of $A$ such that for any two subsets $S_1$ and $S_2$ in $C$, either $S_1 \subset S_2$ or $...

Ishrat Jahan

11.9k views

Ishrat Jahan asked Nov 3, 2014

38 votes

5 answers

12

GATE CSE 1997 | Question: 3.4
Given $\Sigma=\{a,b\}$, which one of the following sets is not countable? Set of all strings over $\Sigma$ Set of all languages over $\Sigma$ Set of all regular languages over $\Sigma$ Set of all languages over $\Sigma$ accepted by Turing machines

Given $\Sigma=\{a,b\}$, which one of the following sets is not countable?Set of all strings over $\Sigma$Set of all languages over $\Sigma$Set of all regular languages ov...

Kathleen

12.4k views

Kathleen asked Sep 29, 2014

20 votes

2 answers

13

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 8
Which of the following is/are true? If $S$ is a set and $|S| = 103$, then $S$ is not the power set of any set (that is, there is no set $T$ where $S = \mathcal{P}(T))$. If $S$ is a set and $|S| = 103$, then $S$ is a power set ... $S$ is not the power set of any set (that is, there is no set $T$ where $S = \mathcal{P}(T))$.

Which of the following is/are true?If $S$ is a set and $|S| = 103$, then $S$ is not the power set of any set (that is, there is no set $T$ where $S = \mathcal{P}(T))$.If ...

GO Classes

231 views

GO Classes asked Apr 3

2 votes

2 answers

14

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 ___________.

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} \ti...

Arjun

2.1k views

Arjun asked Feb 16

46 votes

4 answers

15

GATE CSE 1996 | Question: 2.4
Which one of the following is false? The set of all bijective functions on a finite set forms a group under function composition The set $\{1, 2, \dots p-1\}$ forms a group under multiplication mod $p$, where $p$ is a prime number The set of all strings over a finite ... $\langle G, * \rangle$ if and only if for any pair of elements $a, b \in S, a * b^{-1} \in S$

Which one of the following is false?The set of all bijective functions on a finite set forms a group under function compositionThe set $\{1, 2, \dots p-1\}$ forms a group...

Kathleen

9.6k views

Kathleen asked Oct 9, 2014

43 votes

5 answers

16

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

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 no...

Rucha Shelke

9.9k views

Rucha Shelke asked Sep 16, 2014

12 votes

1 answer

17

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 10
Which of the following statements is /are False? $\{2,3,4\} \in A$ and $\{2,3\} \in B$ implies that $\{4\} \subseteq A-B$. $A \cap B \supseteq\{2,3,4\}$ implies that $\{2,3,4\} \subseteq A$ and $\{2,3,4\} \subseteq B$ ... $\{2,3\} \subseteq A \cup B$ implies that if $\{2,3\} \cap A=\emptyset$ then $\{2,3\} \subseteq B$.

Which of the following statements is /are False?$\{2,3,4\} \in A$ and $\{2,3\} \in B$ implies that $\{4\} \subseteq A-B$.$A \cap B \supseteq\{2,3,4\}$ implies that $\{2,3...

GO Classes

244 views

GO Classes asked Apr 3

54 votes

5 answers

18

GATE CSE 2001 | Question: 2.2
Consider the following statements: $S_1:$ There exists infinite sets $A$, $B$, $C$ such that $A \cap (B \cup C)$ is finite. $S_2:$ There exists two irrational numbers $x$ and y such that $(x+y)$ ... $S_2$? Only $S_1$ is correct Only $S_2$ is correct Both $S_1$ and $S_2$ are correct None of $S_1$ and $S_2$ is correct

Consider the following statements:$S_1:$ There exists infinite sets $A$, $B$, $C$ such that $A \cap (B \cup C)$ is finite.$S_2:$ There exists two irrational numbers $x$ a...

Kathleen

8.9k views

Kathleen asked Sep 14, 2014

11 votes

1 answer

19

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 7
Power set of empty set has exactly _______ subsets. One Two Zero Three

Power set of empty set has exactly _______ subsets.OneTwoZeroThree

GO Classes

176 views

GO Classes asked Apr 3

5 votes

2 answers

20

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 6
Let $S$ be an infinite set and $S_1 \dots , S_n$ be sets such that $S_1 \cup S_2 \cup \dots \cup S_n = S$. Then at least one of the sets $S_i$ is a finite set not more than one of the sets $S_i$ can be finite at least one of the sets $S_i$ is an infinite None of the above

Let $S$ be an infinite set and $S_1 \dots , S_n$ be sets such that $S_1 \cup S_2 \cup \dots \cup S_n = S$. Thenat least one of the sets $S_i$ is a finite setnot more than...

GO Classes

74 views

GO Classes asked Apr 3

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