Search results for discrete-mathematics / GATE Overflow for GATE CSE

33 votes

14 answers

1

GATE CSE 2019 | Question: 12
Let $G$ be an undirected complete graph on $n$ vertices, where $n > 2$. Then, the number of different Hamiltonian cycles in $G$ is equal to $n!$ $(n-1)!$ $1$ $\frac{(n-1)!}{2}$

Let $G$ be an undirected complete graph on $n$ vertices, where $n 2$. Then, the number of different Hamiltonian cycles in $G$ is equal to$n!$$(n-1)!$$1$$\frac{(n-1)!}{2}...

Arjun

21.3k views

Arjun asked Feb 7, 2019

0 votes

3 answers

2

NIELIT 2017 July Scientist B (IT) - Section B: 2
Which of the following is an advantage of adjacency list representation over adjacency matrix representation of a graph? In adjacency list representation, space is saved for sparse graphs. Deleting a vertex in adjacency list ... Adding a vertex in adjacency list representation is easier than adjacency matrix representation. All of the option.

Which of the following is an advantage of adjacency list representation over adjacency matrix representation of a graph?In adjacency list representation, space is saved f...

admin

17.8k views

admin asked Mar 30, 2020

40 votes

6 answers

3

GATE CSE 2019 | Question: 38
Let $G$ be any connected, weighted, undirected graph. $G$ has a unique minimum spanning tree, if no two edges of $G$ have the same weight. $G$ has a unique minimum spanning tree, if, for every cut of $G$, there is a unique minimum-weight edge crossing the cut. Which of the following statements is/are TRUE? I only II only Both I and II Neither I nor II

Let $G$ be any connected, weighted, undirected graph.$G$ has a unique minimum spanning tree, if no two edges of $G$ have the same weight.$G$ has a unique minimum spanning...

Arjun

20.5k views

Arjun asked Feb 7, 2019

68 votes

10 answers

4

GATE CSE 2019 | Question: 35
Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z | x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z | w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ denotes ... of all integers Which of the above sets satisfy $\varphi$? $S_1$ and $S_2$ $S_1$ and $S_3$ $S_2$ and $S_3$ $S_1, S_2$ and $S_3$

Consider the first order predicate formula $\varphi$:$\forall x [ ( \forall z \: z | x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w x) \wedge (\forall z \:...

Arjun

20.1k views

Arjun asked Feb 7, 2019

38 votes

9 answers

5

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

0 votes

2 answers

6

Discrete Mathematics and Its Applications by Kenneth H. Rosen
From where can i get full solution of Discrete Mathematics and Its Applications by Kenneth H. Rosen ?

From where can i get full solution of Discrete Mathematics and Its Applications by Kenneth H. Rosen ?

kaleen bhaiya

18.7k views

kaleen bhaiya asked Jan 23, 2022

16 votes

3 answers

7

number of perfect matching in complete graph
Is there a way to find no of perfect matchings in a complete graph Kn where n could be either even or odd..?

Is there a way to find no of perfect matchings in a complete graph Kn where n could be either even or odd..?

dhingrak

10.8k views

dhingrak asked Dec 2, 2014

36 votes

5 answers

8

GATE CSE 2007 | Question: 85
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move to either $(i + 1, j)$ or $(i,j + 1)$. Suppose that the robot is not allowed to traverse the ... $^{20}\mathrm{C}_{10} - ^{8}\mathrm{C}_{4}\times ^{11}\mathrm{C}_{5}$

Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move...

go_editor

9.5k views

go_editor asked Apr 23, 2016

5 votes

1 answer

9

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 8
Let $A=\{0,1\} \times\{0,1\}$ and $B=\{a, b, c\}$. Suppose $A$ is listed in lexicographic order based on $0<1$ and $B$ is in alphabetic order. If $A \times B \times A$ is listed in lexicographic order, then the next element after $((1,0), c,(1,1))$ is $((1,0), a,(0,0))$ $((1,1), c,(0,0))$ $((1,1), a,(0,0))$ $((1,1), a,(1,1))$

Let $A=\{0,1\} \times\{0,1\}$ and $B=\{a, b, c\}$. Suppose $A$ is listed in lexicographic order based on $0<1$ and $B$ is in alphabetic order. If $A \times B \times A$ is...

GO Classes

65 views

GO Classes asked Apr 10

2 votes

3 answers

10

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 5
Let $\mathrm{A}$ be a finite set of size $\mathrm{n}$. The number of elements in the power set of $A \times A$ is: $2^{n^2}$ $\left(2^n\right)^2$ $\left(2^2\right)^n$ None of the above

Let $\mathrm{A}$ be a finite set of size $\mathrm{n}$. The number of elements in the power set of $A \times A$ is:$2^{n^2}$$\left(2^n\right)^2$$\left(2^2\right)^n$None of...

GO Classes

43 views

GO Classes asked Apr 10

3 votes

1 answer

11

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 4
Let $\mathcal{P}(A)$ denote the power set of $A$. If $\mathcal{P}(A) \subseteq B$ then $2^{|A|} \leq|B|$ $2^{|A|} \geq|B|$ $2|A|<|B|$ $2^{|A|} \geq 2^{|B|}$

Let $\mathcal{P}(A)$ denote the power set of $A$. If $\mathcal{P}(A) \subseteq B$ then$2^{|A|} \leq|B|$$2^{|A|} \geq|B|$$2|A|<|B|$$2^{|A|} \geq 2^{|B|}$

GO Classes

39 views

GO Classes asked Apr 10

3 votes

1 answer

12

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 7
Let $A$ and $B$ be sets in a finite universal set $U$. Given the following : $|A-B|,|A \oplus B|,|A|+|B|$, and $|A \cup B|$ Which of the following is in order of increasing size ? $|A-B|<|A \oplus B|<|A|+|B|<|A \cup B|$ ... $|A-B|<|A \oplus B|<|A \cup B|<|A|+|B|$

Let $A$ and $B$ be sets in a finite universal set $U$. Given the following : $|A-B|,|A \oplus B|,|A|+|B|$, and $|A \cup B|$ Which of the following is in order of increasi...

GO Classes

59 views

GO Classes asked Apr 10

3 votes

0 answers

13

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 9
Which of the following statements is $\textbf{TRUE}$? For all sets $A, B$, and $C, A-(B-C)=(A-B)-C$. For all sets $A, B$, and $C,(A-B) \cap(C-B)=(A \cap C)-B$. For all sets $A, B$, and $C,(A-B) \cap(C-B)=A-(B \cup C)$. For all sets $A, B$, and $C$, if $A \cap C=B \cap C$ then $A=B$.

Which of the following statements is $\textbf{TRUE}$?For all sets $A, B$, and $C, A-(B-C)=(A-B)-C$.For all sets $A, B$, and $C,(A-B) \cap(C-B)=(A \cap C)-B$.For all sets ...

GO Classes

51 views

GO Classes asked Apr 10

2 votes

1 answer

14

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 3
What is the Cartesian product of $A=\{1,2\}$ and $B=\{a, b\}$ ? $\{(1, a),(1, b),(2, a),(b, b)\}$ $\{(1,1),(2,2),(a, a),(b, b)\}$ $\{(1, a),(2, a),(1, b),(2, b)\}$ $\{(1,1),(a, a),(2, a),(1, b)\}$

What is the Cartesian product of $A=\{1,2\}$ and $B=\{a, b\}$ ?$\{(1, a),(1, b),(2, a),(b, b)\}$$\{(1,1),(2,2),(a, a),(b, b)\}$$\{(1, a),(2, a),(1, b),(2, b)\}$$\{(1,1),(...

GO Classes

39 views

GO Classes asked Apr 10

1 votes

2 answers

15

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 2
The cardinality of the power set of $A \cup B$, where $A=\{2,3,5,7\}$ and $B=\{2$, $5,8,9\}$, is?

The cardinality of the power set of $A \cup B$, where $A=\{2,3,5,7\}$ and $B=\{2$, $5,8,9\}$, is?

GO Classes

43 views

GO Classes asked Apr 10

1 votes

1 answer

16

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 1
If $A$ and $B$ are two sets and $A \cup B = A \cap B$ then $A=\phi$ $B=\phi$ $A\neq B$ $A=B$

If $A$ and $B$ are two sets and $A \cup B = A \cap B$ then$A=\phi$$B=\phi$$A\neq B$$A=B$

GO Classes

42 views

GO Classes asked Apr 10

0 votes

1 answer

17

self doubt
how to check the validity of an a argument using laws of logics

how to check the validity of an a argument using laws of logics

farhan777

34 views

farhan777 asked 5 days ago

1 votes

1 answer

18

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 6
Which one of the following is/are true? $R \cap S=(R \cup S)-[(R-S) \cup(S-R)]$ $R \cup S=(R \cap S)-[(R-S) \cup(S-R)]$ $R \cap S=(R \cup S)-[(R-S) \cap(S-R)]$ $R \cap S=(R \cup S) \cup(R-S)$

Which one of the following is/are true?$R \cap S=(R \cup S)-[(R-S) \cup(S-R)]$$R \cup S=(R \cap S)-[(R-S) \cup(S-R)]$$R \cap S=(R \cup S)-[(R-S) \cap(S-R)]$$R \cap S=(R \...

GO Classes

24 views

GO Classes asked Apr 10

1 votes

0 answers

19

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 10
Which of the following statements is $\textbf{FALSE}$? $C-(B \cup A)=(C-B)-A$ $A-(C \cup B)=(A-B)-C$ $B-(A \cup C)=(B-C)-A$ $A-(B \cup C)=(B-C)-A$

Which of the following statements is $\textbf{FALSE}$?$C-(B \cup A)=(C-B)-A$$A-(C \cup B)=(A-B)-C$$B-(A \cup C)=(B-C)-A$$A-(B \cup C)=(B-C)-A$

GO Classes

38 views

GO Classes asked Apr 10

0 votes

0 answers

20

Discrete Mathematics | Set Theory | Relation | Equivalance Relation
which if the following statement is True for every set? a. $\exists$ a equivalence class that is also a partition set. b. Every equivalence relation on a set defines a partition of that set. c. $\exists$ a partition of a set that is also equal to equivalence class of the set on some equivalence relation.

which if the following statement is True for every set?a. $\exists$ a equivalence class that is also a partition set.b. Every equivalence relation on a set defines a part...

RahulVerma3

43 views

RahulVerma3 asked Apr 12

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