Recent questions in Discrete Mathematics

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1

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

asked 1 day ago in Set Theory & Algebra by himgta Active (3.6k points) | 29 views

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2

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

asked 1 day ago in Set Theory & Algebra by himgta Active (3.6k points) | 23 views

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3

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

asked 1 day ago in Set Theory & Algebra by himgta Active (3.6k points) | 43 views

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4

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 2 days ago in Graph Theory by Sayan Bose Loyal (5.9k points) | 29 views

+1 vote

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5

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 2 days ago in Set Theory & Algebra by vivek_mishra (399 points) | 41 views

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6

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 2 days ago in Set Theory & Algebra by dan31 Junior (657 points) | 60 views

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7

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

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8

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

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1 answer

9

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]

asked 3 days ago in Combinatory by Ram Swaroop Active (2.2k points) | 21 views

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1 answer

10

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?

asked 4 days ago in Mathematical Logic by Ravi kumar singh Junior (893 points) | 23 views

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1 answer

11

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

asked 4 days ago in Mathematical Logic by Umang Tamrakar (7 points) | 34 views

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1 answer

12

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

asked 4 days ago in Set Theory & Algebra by sripo Active (1.5k points) | 58 views

+2 votes

1 answer

13

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

asked 4 days ago in Set Theory & Algebra by sripo Active (1.5k points) | 56 views

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1 answer

14

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.

asked 4 days ago in Set Theory & Algebra by sripo Active (1.5k points) | 17 views

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1 answer

15

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?

asked 5 days ago in Mathematical Logic by mehul vaidya Active (3k points) | 30 views

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1 answer

16

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:

asked 6 days ago in Mathematical Logic by Rackson Active (1.8k points) | 56 views

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1 answer

17

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 "

asked Feb 12 in Mathematical Logic by Ankit Jaiswal (7 points) | 20 views

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18

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) | 28 views

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1 answer

19

Self Doubt
From a group of 5 woman and 7 man we have to select a committee consisting of 2 woman and 3 men. Find the total number of ways to select such committed if (1 and 2 are a separate question) 1. Four man refuse to be in the same committee 2. 2 woman refuse to be in the same committee.

asked Feb 8 in Combinatory by smsubham Loyal (9.1k points) | 49 views

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20

#DiscreteMathematics #Rosen #BinomialTheorem
$\sum_{k=0}^{\propto }\left ( \sum_{j=0}^{k}1 \right )x^{k} = \sum_{k=0}^{\propto}(k+1)x^{k}$ How LHS=RHS here?

asked Feb 8 in Mathematical Logic by Reshu $ingh (329 points) | 47 views

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1 answer

21

#Basic #DiscreteMathematics #KennethRosen
Suppose that there are 9 faculty members in the mathematics department and 11 in the computer science department. How many ways are there to select a committee to develop a discrete mathematics course at a school if the committee is to consist of ... use Sum rule. How to decide on Product rule or Sum rule? Please use some basic example for both the cases.

asked Feb 7 in Mathematical Logic by Reshu $ingh (329 points) | 134 views

+1 vote

1 answer

22

GATE2019-5
Let $U = \{1, 2, \dots , n\}$ Let $A=\{(x, X) \mid x \in X, X \subseteq U \}$. Consider the following two statements on $\mid A \mid$. $\mid A \mid = n2^{n-1}$ $\mid A \mid = \Sigma_{k=1}^n k \begin{pmatrix} n \\ k \end{pmatrix}$ Which of the above statements is/are TRUE? Only I Only II Both I and II Neither I nor II

asked Feb 7 in Combinatory by Arjun Veteran (384k points) | 1.9k views

+1 vote

4 answers

23

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 $R_2$

asked Feb 7 in Set Theory & Algebra by Arjun Veteran (384k points) | 1.8k views

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4 answers

24

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

asked Feb 7 in Graph Theory by Arjun Veteran (384k points) | 1.9k views

+2 votes

5 answers

25

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

asked Feb 7 in Mathematical Logic by Arjun Veteran (384k points) | 1.9k views

+1 vote

1 answer

26

GATE2019-38
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

asked Feb 7 in Graph Theory by Arjun Veteran (384k points) | 1.9k views

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1 answer

27

GATE 2019 8
Q.8 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 1. (n-1)!/2 2. 1 3.(n-1)! 4. n!

asked Feb 7 in Graph Theory by Ram Swaroop Active (2.2k points) | 202 views

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2 answers

28

#DiscreteMathematics #Rosen
“For every person x, if person x is a student in this class then x has studied Calculus.” S(x):Person x in the class C(x):x has studied Calculus. 1.$\vartheta _{x} (S(x) --> C(x))$ 2.$\vartheta _{x} (S(x) \Lambda C(x))$ Which one should hold? Why and why not?

asked Feb 7 in Mathematical Logic by Reshu $ingh (329 points) | 62 views

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1 answer

29

Gate CS 2019
S1=Matrix is Invertible S2=Determinant of matrix is Non-zero What is the Answer..

asked Feb 5 in Mathematical Logic by rhtsya (51 points) | 252 views

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1 answer

30

GATE 2019
SOLVE: 2^32 mod 5

asked Feb 5 in Mathematical Logic by IITB2020 (189 points) | 230 views

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