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Recent questions and answers in Discrete Mathematics

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2 answers

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GO Classes 2023 | Weekly Quiz 3 | Question: 12
An island has two kinds of inhabitants, knights, who always tell the truth, and knaves, who always lie. You encounter two people $A$ and $B$. What are $A$ and $B$ if: $A$ says $B$ is a knight and $B$ says The two of us are opposite types ? $A$ is ... , $B$ is knight $B$ is knight, $B$ is knave. $A$ is knave, $B$ is knave. $A$ is knave, $B$ is knight

Udhay_Brahmi answered in Mathematical Logic 5 hours ago

by Udhay_Brahmi

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1 answer

2

NPTEL Assignment
In how many ways can the word ‘DOCUMENTATION’ be arranged so that all the consonants come together.

Coding skill answered in Combinatory 3 days ago

by Coding skill

92 views

0 votes

1 answer

3

maths igate test series
Which of the relations below can also be characterized as a function defined on the set I = { 1, 2, 3, 4, 5 } { (x, y) | x, y ∈ I, x < y } B{ (x, y) | x, y ∈ I, x = 1 } C{ (x, y) | x, y ∈ I, x! = y } None of these

Aditya_ answered in Set Theory & Algebra 3 days ago

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0 votes

1 answer

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Kenneth Rosen Edition 7 Exercise 6.5 Question 59 (Page No. 434)
How many ways are there to distribute five balls into three boxes if each box must have at least one ball in it if both the balls and boxes are labeled? the balls are labeled, but the boxes are unlabeled? the balls are unlabeled, but the boxes are labeled? both the balls and boxes are unlabeled?

ankit-saha answered in Combinatory 4 days ago

119 views

1 vote

1 answer

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Kenneth Rosen Edition 7 Exercise 6.5 Question 58 (Page No. 434)
How many ways are there to distribute five balls into seven boxes if each box must have at most one ball in it if both the balls and boxes are labeled? the balls are labeled, but the boxes are unlabeled? the balls are unlabeled, but the boxes are labeled? both the balls and boxes are unlabeled?

ankit-saha answered in Combinatory 4 days ago

164 views

0 votes

1 answer

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Kenneth Rosen Edition 7 Exercise 6.5 Question 57 (Page No. 434)
How many ways are there to pack nine identical DVDs into three indistinguishable boxes so that each box contains at least two DVDs?

ankit-saha answered in Combinatory 4 days ago

102 views

1 vote

1 answer

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Kenneth Rosen Edition 7 Exercise 6.5 Question 56 (Page No. 434)
How many ways are there to pack eight identical DVDs into five indistinguishable boxes so that each box contains at least one DVD?

ankit-saha answered in Combinatory 4 days ago

112 views

50 votes

5 answers

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GATE CSE 2003 | Question: 31
Let $(S, \leq)$ be a partial order with two minimal elements a and b, and a maximum element c. Let P: S \(\to\) {True, False} be a predicate defined on S. Suppose that P(a) = True, P(b) = False and P(x) \(\implies\) P(y) for all $x, y \in S$ satisfying $x \leq y$ ... for all x \(\in\) S such that b ≤ x and x ≠ c P(x) = False for all x \(\in\) S such that a ≤ x and b ≤ x

[ Jiren ] answered in Set Theory & Algebra Aug 12

8.1k views

1 vote

1 answer

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Kenneth Rosen Edition 7 Exercise 6.1 Question 41 (Page No. 397)
A palindrome is a string whose reversal is identical to the string. How many bit strings of length $n$ are palindromes?

ankit-saha answered in Combinatory Aug 11

114 views

1 vote

1 answer

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Kenneth Rosen Edition 7 Exercise 6.1 Question 40 (Page No. 397)
How many subsets of a set with $100$ elements have more than one element?

ankit-saha answered in Combinatory Aug 11

71 views

55 votes

14 answers

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GATE CSE 2015 Set 3 | Question: 5
The number of $4$ digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set $\{1, 2, 3\}$ is ________.

Himanshu555 answered in Combinatory Aug 11

10.5k views

3 votes

2 answers

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GO Classes Scholarship 2023 | Test | Question: 11
Let $\text{U}$ be a set and $\text{X, Y} \subseteq \text{U}$. Define operation twist by $ \operatorname{twist}\text{(X, Y)} =(\text{X} \cap \text{Y}) \cup(\overline{\text{X}} \cap \overline{\text{Y}}). $ Which of the following ... $\operatorname{twist}\text{(X, Y)}=\operatorname{twist}(\overline{\text{X}}, \overline{\text{Y}})$

[ Jiren ] answered in Set Theory & Algebra Aug 9

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2 votes

3 answers

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GO Classes Scholarship 2023 | Test | Question: 2
Let $\text{S}$ be the set of all bit-strings of length $7 .$ We define a relation $\mathrm{R}$ on the set $\mathrm{S}$ by the rule that $x\mathrm{R}y$ iff $x$ and $y$ ... such that $\forall j \neq i, x_{j}=y_{j}$ and $x_{i} \neq y_{i}$. What is the cardinality of relation $\mathrm{R}$?

Godlike answered in Set Theory & Algebra Aug 9

321 views

4 votes

2 answers

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GO Classes Scholarship 2023 | Test | Question: 4
Consider a $3 \times 11$ rectangular grid as depicted in Figure $1,$ formed by $33$ tiles of area $1\text{m}^2.$ A staircase walk is a path in the grid which moves only right or up. How many staircase walks are there from $\text{A}$ to $\text{B}$ which start by going to the right two times?

[ Jiren ] answered in Combinatory Aug 8

192 views

53 votes

8 answers

15

GATE CSE 2013 | Question: 26
The line graph $L(G)$ of a simple graph $G$ is defined as follows: There is exactly one vertex $v(e)$ in $L(G)$ for each edge $e$ in $G$. For any two edges $e$ and $e'$ in $G$, $L(G)$ has an edge between $v(e)$ and $v(e')$, if and only if $e$ ... of a planar graph is planar. (S) The line graph of a tree is a tree. $P$ only $P$ and $R$ only $R$ only $P, Q$ and $S$ only

Jyotish Ranjan answered in Graph Theory Aug 7

by Jyotish Ranjan

14.2k views

4 votes

2 answers

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GO Classes Scholarship 2023 | Test | Question: 9
Consider the following graph $\text{G:}$ Let $\text{M, C, I, S, B, E}$ be the Matching number, chromatic number, independence number, Clique number, Vertex cover number, and edge cover number, respectively of $\text{G}.$ What is $\text{M+C+I+S+B+E}?$

Kabir5454 answered in Graph Theory Aug 7

162 views

3 votes

1 answer

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GO Classes Scholarship 2023 | Test | Question: 1
A relation $\text{R}$ on a set $\text{A}$ is said to be Total Relation iff $a\text{R}b$ Or $b\text{R}a$ Or both, for all $a,b \in \mathrm{A}$. Which of the following options is/are false? Every Total relation is ... total and transitive, then $\mathrm{S}$ is an equivalence relation. The number of total relations on a set of $5$ elements is $1024.$

GO Classes answered in Set Theory & Algebra Aug 7

393 views

4 votes

1 answer

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GO Classes Scholarship 2023 | Test | Question: 3
Let $\text{A, B}$ be two disjoint non-empty sets. Let $\text{M}$ be the universal set and $\text{A} \cup \text{B}$ is a proper subset of $\mathrm{M}$. For any set $\mathrm{S}$, let $\mathrm{S}^{\prime}$ be the set of those elements ...

GO Classes answered in Set Theory & Algebra Aug 7

186 views

2 votes

1 answer

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GO Classes Scholarship 2023 | Test | Question: 5
Consider $5$ cards, each has a distinct value from the set $\{2,3,4,5,6\},$ so there are $5$ different values, and we put them face down on the table. There are $5$ players and each player is given a number from $2$ ... with the value that player has. If no player loses, then the dealer loses. How many ways are there so that the dealer loses?

GO Classes answered in Combinatory Aug 7

138 views

4 votes

1 answer

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GO Classes Scholarship 2023 | Test | Question: 6
Consider three boxes and $12$ balls of the same size. We have $3$ indistinguishable red balls and $9$ distinguishable blue balls. The first box can fit at most three balls, the second box can fit at most four balls and the third box can fit ... all the red balls go into the same box. What is the total number of ways to put all the balls in the boxes?

GO Classes answered in Combinatory Aug 7

146 views

2 votes

1 answer

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GO Classes Scholarship 2023 | Test | Question: 7
Define the generating functions $\text{B}(x)=\displaystyle{} \sum_{n=0}^{\infty} 2^{n} x^{n}$ and $F(x)=\displaystyle{} \sum_{n=0}^{\infty} f_{n} x^{n}$ where $f_{n}$ ... $x^{5}$ is $\mathrm{G}(x)?$

GO Classes answered in Combinatory Aug 7

126 views

3 votes

1 answer

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GO Classes Scholarship 2023 | Test | Question: 8
In a directed graph $\mathrm{G}=(\mathrm{V}, \mathrm{E})$, two nodes $u$ and $v$ are strongly connected if and only if they are mutually reachable i.e. there is a path from u to $v$ and a path from $v$ to $u$. ... connected components $\dots?$ can not increase can not decrease by more than $1$ can not decrease by more than $2$ may remain unchanged

GO Classes answered in Graph Theory Aug 7

110 views

3 votes

1 answer

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GO Classes Scholarship 2023 | Test | Question: 10
For which of the following does there exist a graph satisfying the specified conditions? A tree with six vertices and six edges. A tree with three or more vertices, two vertices of degree one, and all the other vertices with degree three or ... with $10$ vertices and $8$ edges. A disconnected graph with $12$ vertices and $11$ edges and no cycle.

GO Classes answered in Graph Theory Aug 7

114 views

4 votes

1 answer

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GO Classes Scholarship 2023 | Test | Question: 12
How many non-isomorphic simple undirected graphs are there, each with four vertices and without a cycle?

GO Classes answered in Graph Theory Aug 7

111 views

4 votes

1 answer

25

GO Classes Scholarship 2023 | Test | Question: 13
Let $\text{T}_{n}$ be the number of ways to arrange cars in a row with $n$ parking spaces if we can use sedans, SUVs, trucks to park such that a truck requires two spaces, whereas a sedan or SUV requires just one space each, and No two ... i.e. initial conditions are already given, hence no need to compute them)

GO Classes answered in Combinatory Aug 7

176 views

1 vote

2 answers

26

GO Classes 2023 | Weekly Quiz 3 | Question: 20
The implies connective $\rightarrow$ is one of the stranger connectives in propositional logic. Below are a series of statements regarding implications. Which of the following statements is/are TRUE? For any propositions $P$ and $Q,$ the following is ... $R,$ the following statement is always true: $(P \rightarrow Q) \vee (R \rightarrow Q)$.

P SHANMUKHA SHARMA answered in Mathematical Logic Aug 6

by P SHANMUKHA SHARMA

144 views

0 votes

1 answer

27

Self doubt : Set Theory
At a family group meeting of 30 women, 17 are descended from George, 16 are descended from John, and 5 are not descended from George or John. How many of the 30 women are descended from both George and John?

Aditya_ answered in Set Theory & Algebra Aug 4

68 views

62 votes

12 answers

28

GATE CSE 1994 | Question: 1.6, ISRO2008-29
The number of distinct simple graphs with up to three nodes is $15$ $10$ $7$ $9$

Cs_Gate_22 answered in Graph Theory Aug 4

26.4k views

54 votes

13 answers

29

GATE CSE 2014 Set 1 | Question: 49
A pennant is a sequence of numbers, each number being $1$ or $2$. An $n-$pennant is a sequence of numbers with sum equal to $n$. For example, $(1,1,2)$ is a $4-$pennant. The set of all possible $1-$pennants is ${(1)}$, the set of all possible ... $(1,2)$ is not the same as the pennant $(2,1)$. The number of $10-$pennants is________

Argharupa Adhikary answered in Combinatory Jul 31

by Argharupa Adhikary

7.0k views

43 votes

7 answers

30

GATE CSE 2007 | Question: 84
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 $(i,j + 1)$. How many distinct paths are there for the ... $(10,10)$ starting from the initial position $(0,0)$? $^{20}\mathrm{C}_{10}$ $2^{20}$ $2^{10}$ None of the above

Argharupa Adhikary answered in Combinatory Jul 31

by Argharupa Adhikary

8.7k views

0 votes

1 answer

31

Mathematics for Natural Science
Prove that $2n < (n + 1)!, $ for all $ n \geq 3.$

Kabir5454 answered in Combinatory Jul 29

43 views

15 votes

5 answers

32

GATE CSE 2002 | Question: 3
Let $A$ be a set of $n(>0)$ elements. Let $N_r$ be the number of binary relations on $A$ and let $N_f$ be the number of functions from $A$ to $A$ Give the expression for $N_r,$ in terms of $n.$ Give the expression for $N_f,$ terms of $n.$ Which is larger for all possible $n,N_r$ or $N_f$

Genius answered in Set Theory & Algebra Jul 29

by Genius

2.9k views

0 votes

1 answer

33

Mathematics for Natural Science
Simplify $(A\cup B)\cap (A\cup B')\cap (A - B)$ for a given non empty sets $A$ and $B$, where $(A\cap B) = \varnothing .$

Kabir5454 answered in Combinatory Jul 29

38 views

0 votes

0 answers

34

Mathematics for Natural Science
Let y in the form of $a + bi$, where $a$ and $b$ are real numbers, be the cubic roots of complex number $z^{20},$ where $z=\frac{2}{4 + 3i}.$ Find $a + b.$

kidussss asked in Combinatory Jul 29

47 views

0 votes

0 answers

35

Mathematics for Natural Science
Suppose $x, y, z > 1$ are integers, let: $p(x,y)$ : $x$ is a factor of $y$ $q(x,y,z)$ : $z$ = $\text{GCD}(x,y)$ $r(x)$ : $x$ is prime. Check if the following argument is valid or not. $(\forall x \exists y)p(x,y) \implies r(x)$ ... $(\exists x)(\forall y)(p(x,y) \lor r(x))$ $\therefore (\forall y)(\exists z)(\exists x)q(x,y,z)$

kidussss asked in Mathematical Logic Jul 29

53 views

35 votes

8 answers

36

GATE CSE 2009 | Question: 22
For the composition table of a cyclic group shown below: ... $a,b$ are generators $b,c$ are generators $c,d$ are generators $d,a$ are generators

Argharupa Adhikary answered in Set Theory & Algebra Jul 26

by Argharupa Adhikary

6.2k views

1 vote

1 answer

37

Made Easy Test Series
How to solve this question?

Aditya_ answered in Mathematical Logic Jul 25

145 views

1 vote

3 answers

38

GO Classes Weekly Quiz 2 | Programming in C | Propositional Logic | Question: 11
Let $P,S,R$ be three statements(propositions). Let $S$ be a sufficient condition for $P$, Let $R$ is a necessary condition for $P$ then which of the following is/are true? $S$ is a sufficient condition ... is neither sufficient, nor a necessary condition for $R.$ $S$ is a sufficient and necessary condition for $R$.

Argharupa Adhikary answered in Mathematical Logic Jul 25

by Argharupa Adhikary

181 views

0 votes

1 answer

39

Cengage algebra jee advanced.
Coefficient of x^8 in ( (1-x^6)/(1-x) )^3.

Kabir5454 answered in Combinatory Jul 24

88 views

0 votes

1 answer

40

Self Doubt - Planarity of Complete Bipartite Graph
How to determine for which m, n the complete bipartite graph $Km,n$ is planar? I am getting two answers from two sources:- A complete bipartite graph $Kmn$ is planar if and only if m<3 or n>3. Source: https://www.javatpoint.com/ ... m ≤ 2 or n ≤ 2. Source: http://www.matthewkahle.org/download/file/fid/573 Need a proper proof of the solution.

Abhrajyoti00 asked in Graph Theory Jul 21

by Abhrajyoti00

63 views

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Recent questions and answers in Discrete Mathematics