Recent questions and answers in Discrete Mathematics

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1

Rosen example 12 Ch 5.2
Show that every sequence of $n^2$+1 distinct real numbers contains a subsequence of length n+1 that is either strictly increasing or strictly decreasing.

asked 1 hour ago in Combinatory by himgta Active (3.6k points) | 10 views

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1 answer

2

Rosen
S(x): x is a student F(X): x is a faculty member A(x, y): x has asked y a question use quantifiers to express: Some student has asked every faculty member a question

answered 10 hours ago in Mathematical Logic by Deepakk Poonia (Dee) Boss (22.8k points) | 21 views

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1 answer

3

Kenneth Rosen Example 9 Ch.5.2
Suppose that a computer science laboratory has 15 workstations and 10 servers. A cable can be used to directly connect a workstation to a server. For each server, only one direct connection to that server can be active at any time. We ... 't understand this part. How is it concluded that remaining nine servers are insufficient when at most 59 connections are used?

answered 15 hours ago in Combinatory by Deepakk Poonia (Dee) Boss (22.8k points) | 28 views

+1 vote

1 answer

4

Strongly Connected, Unilaterally connected and weakly Connected
Hi Guys, Is there any quick way of verifying Graph is Strongly Connected, Unilaterally connected and weakly Connected ? For Example - If 1 dead point then graph is Unilaterally Connected and If 2 dead points then graph is Weakly Connected.

answered 1 day ago in Graph Theory by saurav raghaw Active (1k points) | 256 views

+2 votes

1 answer

5

kenneth rosen Ex2.4 Q.46
Show that the set of functions from the positive integers to the set {0,1,2,3,4,5,6,7,8,9} is uncountable.

answered 2 days ago in Set Theory & Algebra by Devshree Dubey Boss (13.5k points) | 99 views

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1 answer

6

UGCNET-june2009-ii-25
The prepositional formula given by the tree: is: (A) ˄˅x2˅x1¬x1¬x1 (B) (x2˅¬x2)˄(x1˅x2) (C) (¬x1˅x2)˄(¬x1˅x2) (D) None

answered 2 days ago in Mathematical Logic by rajatmyname Active (1.3k points) | 94 views

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1 answer

7

Logic- Kenneth Rosen Ex1.4 Q.23
what is the approach of solving this question? Q.Translate in two ways each of these statements into logical expressions using predicates, quantifiers, and logical connectives. First, let the domain consist of the students in your class and second, let it ... in your class has been in a movie. e) No student in your class has taken a course in logic programming.

answered 2 days ago in Mathematical Logic by Bhaskar Singh (229 points) | 54 views

+1 vote

1 answer

8

ISI MMA-2015-27
Let, $cos^{6}\theta = a_{6}cos6\theta + a_{5}cos5\theta + a_{4}cos4\theta + a_{3}cos3\theta + a_{2}cos2\theta + a_{1}cos\theta + a_{0}$ Then $a_{0}$ is (A) $0$ (B) $\frac{1}{32}$ (C) $\frac{15}{32}$ (D) $\frac{10}{32}$ ... 3 equations , I am getting $a_{0} + a_{4} = \frac{1}{2}$ but don't know how to proceed further to get the value of $a_{0}$. Please help.

answered 2 days ago in Set Theory & Algebra by venkatesh pagadala (415 points) | 77 views

+16 votes

4 answers

9

GATE2000-5
A multiset is an unordered collection of elements where elements may repeat any number of times. The size of a multiset is the number of elements in it, counting repetitions. What is the number of multisets of size $4$ that can be constructed from n distinct elements so that at least one element occurs exactly twice? How many multisets can be constructed from n distinct elements?

answered 4 days ago in Combinatory by Priyadrasta Raut (345 points) | 1.1k views

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1 answer

10

Kenneth rosen Q.36 Ex.2.3
Let f be a function from the set A to the set B.Let S and T be subsets of A.Show that $f(S\cup T)=f(S)\cup f(T)$ $f(S\cap T)\subseteq f(S)\cap f(T)$ Show that inclusion in part b can be proper

answered 5 days ago in Set Theory & Algebra by prashant jha 1 Active (4.1k points) | 40 views

+2 votes

1 answer

11

GATE - 2014 - 1- 51 modified
Consider an directed graph G where self-loops are not allowed. The vertex set of G is {(i,j)∣1≤i≤12,1≤j≤12}There is an edge from(a,b) to (c,d) if |a−c|≤1 and |b−d|≤1. The number of edges in this graph is______

answered 5 days ago in Graph Theory by Priyadrasta Raut (345 points) | 121 views

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1 answer

12

kenneth rosen Ex 2.3 Q.29,30
Justify the statements. 1. if f and f o g are one to one,does it follows that g is one to one. 2 if f and f o g are onto,does it follow that g is onto

answered 5 days ago in Set Theory & Algebra by Deepakk Poonia (Dee) Boss (22.8k points) | 27 views

–1 vote

0 answers

13

Kenneth Rosen Ex.2.3 Q.3(c)
https://prnt.sc/cncgcv plz explain the c part!

asked 5 days ago in Set Theory & Algebra by himgta Active (3.6k points) | 52 views

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14

JEST 2019
A directed graph with n vertices, in which each vertex has exactly 3 outgoing edges. Which one is true? A) All the vertices have indegree = 3 . B) Some vertices will have indegree exactly 3. C)Some vertices have indegree atleast 3. D) Some of the vertices have indegree atmost 3

asked 6 days ago in Graph Theory by Sayan Bose Loyal (5.9k points) | 32 views

+1 vote

0 answers

15

JEST 2019
Let ${(0,1)}^n$ set of all binary string of length n. Hamming sphere of radius around a string C in ${(0,1)}^n$ is the set of all strings d$\epsilon$ ${(0,1)}^n$ that differ from C in at most r of n position, S(C,r) for n=2k+1 For C,C’ $\epsilon$ ${(0,1)}^n$ S(C,k) and S(C’,k) are disjoint couldn't remember rest of the options.

asked 6 days ago in Set Theory & Algebra by vivek_mishra (399 points) | 48 views

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0 answers

16

JEST 2019 Descriptive Q3 (8 Marks)
Determine the number of functions f:{1,2,3…,n}→{1995,1996} satisfying the condition that f(1)+f(2)+…f(n) is odd.

asked 6 days ago in Set Theory & Algebra by dan31 Junior (657 points) | 68 views

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0 answers

17

JEST 2019 Descriptive Q2 (8 Marks)
Given a sequence $a_1$, $a_2$ , $a_3$ ... $a_n$ of any different positive integers, exhibit an arrangement of integers between 1 and $n^2$ which has no increasing or decreasing subsequence of length n+1.

asked 6 days ago in Graph Theory by dan31 Junior (657 points) | 29 views

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18

JEST 2019 Descriptive Q1 (8 Marks)
Suppose that G contains a cycle C, and a path of length at least k between some two vertices of C. Show that G contains a cycle of length at least √k.

asked 6 days ago in Graph Theory by dan31 Junior (657 points) | 24 views

+1 vote

2 answers

19

TIFR-2011-Maths-A-16
The polynomial $x^{4}+7x^{3}-13x^{2}+11x$ has exactly one real root.

answered Feb 16 in Set Theory & Algebra by Sreyasree Mandal (117 points) | 121 views

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1 answer

20

Kenneth Rosen chapter 5 20 discrete mathematics
A playoff between two teams consists of at most five games . The first team that wins three games wins the playoff. In how many different way playoff occur? [closed]

answered Feb 16 in Combinatory by subhrob (373 points) | 30 views

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1 answer

21

Linear algebra
The number of different n×n symmetric matrices with each element being 0 or 1 is

answered Feb 15 in Mathematical Logic by Ananya Jaiswal 1 Active (2.2k points) | 35 views

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1 answer

22

Discrete Maths and Its Applications, 7th Edition, Kenneth Rosen
1. Which of these sentences are propositions? What are the truth values of those that are propositions? a) Boston is the capital of Massachusetts. b) Miami is the capital of Florida. c) 2+3 = 5. d) 5+7 = 10. e) x +2 ... is answer for f) as I am thinking I can answer this question or I will not answer this question is it a proposition?

answered Feb 15 in Mathematical Logic by prashant jha 1 Active (4.1k points) | 25 views

+12 votes

3 answers

23

CMI2013-A-06
A simple graph is one in which there are no self-loops and each pair of distinct vertices is connected by at most one edge.Let $G$ be a simple graph on $8$ vertices such that there is a vertex of degree $1$, a vertex of degree $2$, a vertex of degree $3$, a vertex of ... degree $6$ and a vertex of degree $7$. Which of the following can be the degree of the last vertex? $3$ $0$ $5$ $4$

answered Feb 15 in Graph Theory by Satbir Active (5.1k points) | 562 views

+2 votes

1 answer

24

JEST Sample Question 1-b
When is the following statement true? (A ∪ B) ∩ C = A ∩ C (A) If Ā ∩ B ∩ C = φ (B) If A ∩ B ∩ C = φ (C) always (D) never

answered Feb 15 in Set Theory & Algebra by Ram Swaroop Active (2.3k points) | 56 views

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1 answer

25

JEST Sample Question 1-a
Let a and b be positive integers such that a > b and a^ 2 − b^ 2 is a prime number. Then a^2 − b^ 2 is equal to (A) a − b (B) a + b (C) a × b (D) none of the above

answered Feb 15 in Set Theory & Algebra by Naveen Kumar 3 Active (3.4k points) | 58 views

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1 answer

26

Jest Exam sample question-3
How many subsets of even cardinality does an n-element set have ? Justify answer. Please give a proof if possible.This is part of subjective JEST paper.

answered Feb 15 in Set Theory & Algebra by subhrob (373 points) | 17 views

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1 answer

27

For All & There Exist property
is For All V is distributive on AND operator? ----1 is ‘’there exist’’ is distributive over OR operator? ----2 I have example in which this is true , but is true in general? so logically checking without using any property above four statements are correct. But is 1 and 2 always correct?

answered Feb 15 in Mathematical Logic by Arko Jyoti Shith (37 points) | 31 views

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4 answers

28

GATE2019-12
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 $n!$ $(n-1)!$ $1$ $\frac{(n-1)!}{2}$

answered Feb 14 in Graph Theory by OO7 Junior (579 points) | 2.1k views

0 votes

1 answer

29

Permutation and Combination
The total number of ways in which 5 balls of different color can be distributed among 3 persons so that each person gets at least one ball is:

answered Feb 14 in Mathematical Logic by Satbir Active (5.1k points) | 56 views

+2 votes

5 answers

30

GATE2019-35
Consider the first order predicate formula $\phi$: $\forall x [ ( \forall z \: z \mid x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z \mid w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ denotes ... S2: Set of all positive integers S3: Set of all integers Which of the above sets satisfy $\phi$? S1 and S2 S1 and S3 S2 and S3 S1, S2 and S3

answered Feb 12 in Mathematical Logic by Tuhin Dutta Loyal (9.1k points) | 1.9k views

0 votes

1 answer

31

Rosen ch1 Ex.1.6 Q10.b
What are relevant conclusion and explain rule of inference used ? "If i work ,it is either Sunny or partly sunny." " I worked last Monday or i worked last friday." " It was not Sunny on Tuesday."" It was not partly sunny on Friday "

answered Feb 12 in Mathematical Logic by Deepak Kumar 12 Active (1.6k points) | 21 views

0 votes

0 answers

32

Kenneth Rosen Ex.1.3 Q.37
Express each of these statements using predicates and quantifiers. a) A passenger on an airline qualifies as an elite flyer if the passenger flies more than 25,000 miles in a year or takes more than 25 flights during that year.

asked Feb 10 in Mathematical Logic by himgta Active (3.6k points) | 29 views

+1 vote

4 answers

33

GATE2019-10
Let $G$ be an arbitrary group. Consider the following relations on $G$: $R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a = g^{-1}bg$ $R_2: \forall a , b \in G, \: a R_2 b \text{ if and only if } a= b^{-1}$ Which of the above is/are equivalence relation/relations? $R_1$ and $R_2$ $R_1$ only $R_2$ only Neither $R_1$ nor $R_2$

answered Feb 10 in Set Theory & Algebra by amangarg (63 points) | 1.9k views

+6 votes

4 answers

34

TIFR2018-A-6
What is the minimum number of students needed in a class to guarantee that there are at least $6$ students whose birthdays fall in the same month ? $6$ $23$ $61$ $72$ $91$

answered Feb 10 in Combinatory by Satbir Active (5.1k points) | 311 views

+17 votes

2 answers

35

TIFR2014-A-5
The rules for the University of Bombay five-a-side cricket competition specify that the members of each team must have birthdays in the same month. What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students? $23$ $91$ $60$ $49$ None of the above.

answered Feb 10 in Combinatory by Satbir Active (5.1k points) | 769 views

+15 votes

6 answers

36

TIFR2016-A-15
In a tournament with $7$ teams, each team plays one match with every other team. For each match, the team earns two points if it wins, one point if it ties, and no points if it loses. At the end of all matches, the teams are ordered in the descending order of their ... total number of points a team must earn in order to be guaranteed a place in the next round? $13$ $12$ $11$ $10$ $9$

answered Feb 10 in Combinatory by Satbir Active (5.1k points) | 581 views

+22 votes

6 answers

37

GATE2004-IT-35
In how many ways can we distribute $5$ distinct balls, $B_1$, $B_2$, ..., $B_5$ in $5$ distinct cells, $C_1$, $C_2$, ...., $C_5$ such that Ball $B_i$ is not in cell $C_i$, $\forall i= 1,2,...5$ and each cell contains exactly one ball? $44$ $96$ $120$ $3125$

answered Feb 9 in Combinatory by Satbir Active (5.1k points) | 2.3k views

+7 votes

3 answers

38

TIFR2010-A-4
If the bank receipt is forged, then Mr. M is liable. If Mr. M is liable, he will go bankrupt. If the bank will loan him money, he will not go bankrupt. The bank will loan him money. Which of the following can be concluded from the above statements? Mr. M is liable The receipt is not forged Mr. M will go bankrupt The bank will go bankrupt None of the above

answered Feb 9 in Mathematical Logic by Ram Swaroop Active (2.3k points) | 433 views

+13 votes

3 answers

39

CMI2010-A-02
We need to choose a team of $11$ from a pool of $15$ players and also select a captain. The number of different ways this can be done is $ \begin{pmatrix} 15 \\ 11 \end{pmatrix}$ $11$ . $ \begin{pmatrix} 15 \\ 11 \end{pmatrix}$ $15 . 14 . 13 . 12 . 11 .10 . 9 . 8 . 7 . 6 . 5$ $(15 . 14 . 13 . 12 . 11 .10 . 9 . 8 . 7 . 6 . 5) . 11$

answered Feb 9 in Combinatory by Satbir Active (5.1k points) | 571 views

0 votes

2 answers

40

GATEBOOK-2019-DM1-12
Translate the following logic statement to English where, $A(x)$: $x$ is African, $F(x,y)$: x and y are friends. The universe for $x$ and $y$ is all the people in the world. $\forall x \exists y((A(x) \vee (F(x,y)))$ Every African has some African friend Every person who is not African has at least one friend Every person who has friend is not African None of these

answered Feb 8 in Mathematical Logic by KULDEEP SINGH 2 Junior (727 points) | 148 views

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