Recent questions and answers in Discrete Mathematics

0 votes

2 answers

1

Combinatorics-Kenneth Rosen(Ex 5.3 31)
The english alphabet contains 21 consonants and five vowels.How many strings of six lowercase letters of the English alphabet contain (b)Exactly two vowels (d)At least two vowels For (b) part I solved it like choose 2 vowels from 5 in $\binom{5}{2}$ ways ... }*6!))$ and both of my answers don't match with the key in Rosen. Please let me know where I am wrong.

answered 13 hours ago in Combinatory by srestha Veteran (86.9k points) | 47 views

0 votes

1 answer

2

Combinatorics-Kenneth Rosen(Ex 5.3-41)
How many ways are there for a horse race with three horses to finish if ties are possible.(Two or three horses may tie).

answered 18 hours ago in Combinatory by Anu007 Boss (17k points) | 11 views

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0 answers

3

Combinatorics-Kenneth Rosen (Ex 5.2 12)
How many ordered pairs of integers (a,b) are needed to guarantee that there are two ordered pairs ($a_{1}$,$b_1$) and ($a_2,b_2)$ such that $a_1$ mod 5=$a_2$ mod 5 and $b_1$ mod 5=$b_2$ mod 5? My answer comes to be 26. Please confirm.

asked 1 day ago in Combinatory by Ayush Upadhyaya Loyal (9k points) | 44 views

0 votes

1 answer

4

Combinatorics-Kenneth Rosen(Ex5.1 23c)
How many strings of three decimal digits can be formed such that they have exactly two digits that are 4's. My approach as to select 2 positions for these 4's in $\binom{3}{2}$ ways and the last bit will have 10 choices.Now I can permute the string formed in $ ... total such strings should be $\binom{3}{2}$ * 10*$\frac{3!}{2!}$ = 90. But the answer is 27. How?

answered 1 day ago in Combinatory by Soumya29 Loyal (9.9k points) | 23 views

+1 vote

2 answers

5

Graph Theory Question
Consider a social network with n persons. Two persons A and B are said to be connected if either they are friends or they are related through a sequence of friends: that is, there exists a set of persons F1, . . . , Fm such that A and F1 ... . It is known that there are k persons such that no pair among them is connected. What is the maximum number of friendships possible?

answered 2 days ago in Graph Theory by himanshu19 Junior (691 points) | 232 views

+2 votes

1 answer

6

find close form of generating function discrete mathematics kenneth rosen

answered 2 days ago in Mathematical Logic by neeraj33negi (399 points) | 53 views

+1 vote

2 answers

7

Graph Theory- vertex degree
Consider an undirected graph with n vertices, vertex 1 has degree 1, while each vertex 2,3......, n – 1 has degree 4. The degree of vertex n is unknown. Which of the following statement must be TRUE? a. Vertex n has degree 1. b. Graph is connected. c. There is a path from vertex 1 to vertex n. d. Spanning tree will include the edge connecting vertex 1 and n.

answered 2 days ago in Graph Theory by himanshu19 Junior (691 points) | 131 views

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0 answers

8

Combinatorics-Self doubt
How many outcomes are possible when 10 coins are tossed? $X_{h} + X_{t}$ =10 where $X_{h}$ denotes the number of heads and it is $\geq$0 and $X_{t}$ denotes the number of tails which is also $\geq$0. This comes out to be .$_{10}^{2 ... Shouldn't the answer to the above problem be $2^{10}$ considering each coin can have 2 outcomes either heads or tails? Which one is correct?

asked 2 days ago in Combinatory by Ayush Upadhyaya Loyal (9k points) | 29 views

0 votes

1 answer

9

Combinatorics-Self Doubt
In how many ways can we arrange 4 boys and 3 girls in a straight line such that no two girls are together. One approach came to my mind was arrange 4 boys first=4! ways. Now 5 gaps created.Choose 3 for girls and arrange girls=5C3*3! ... !(total ways without restriction) why am I getting a different answer from the former case where I take boys first and then arrange girls?

answered 2 days ago in Combinatory by Sumeet Singh Junior (501 points) | 28 views

+3 votes

1 answer

10

Graph Coloring
A vertex colouring with four colours of a graph G = (V, E) is a mapping V → {R, G, B, Y }. So that any two adjacent vertices does not same colour. Consider the below graphs: The number of vertex colouring possible with 4 colours are _________. ... Red and D with also blue which is other than Green, now this case is clearly violating graph coloring property. How, to solve this one?

answered 3 days ago in Graph Theory by Prashank (55 points) | 105 views

0 votes

1 answer

11

Rank of a matrix
Let A be a 4×3 real matrix with rank 2. Let B be transpose matrix of A. Which one of the following statement is TRUE? (a) Rank of BA is less than 2. (b) Rank of BA is equal to 2. (c) Rank of BA is greater than 2. (d) Rank of BA can be any number between 1 and 3.

answered 3 days ago in Mathematical Logic by Shubhgupta Junior (669 points) | 20 views

0 votes

0 answers

12

UGCNET-Nov-2017-III-70
Consider a Takagi - Sugeno - Kang (TSK) Model consisting of rules of the form : If x1 is Ai1 and ... and xr is Air THEN y =fi (x1, x2, ..., xr) = bi0+bi1 x1+.....+birxr assume, $\alpha$i is the matching degree of rule i, then the total output of the model is given by : (1) y ... 1}^{L}$ fi (x1,x2,....., xr)/$\sum_{i=1}^{L}\alpha$i (4) y = maxi [$\alpha$i fi (x1,x2,....., xr)]

asked 4 days ago in Mathematical Logic by Roma_nagpal (115 points) | 20 views

0 votes

0 answers

13

This question is from graph theory
What is the total number of vertices in a tree if there are 3n vertices of degree 2 and 2n vertices of degree n?

asked 5 days ago in Mathematical Logic by Pratyush (7 points) | 24 views

+33 votes

7 answers

14

GATE2015-3-24
In a room there are only two types of people, namely Type 1 and Type 2. Type 1 people always tell the truth and Type 2 people always lie. You give a fair coin to a person in that room, without knowing which type he is from and tell him to toss it and hide the ... The result is tail If the person is of Type 2, then the result is tail If the person is of Type 1, then the result is tail

answered 5 days ago in Mathematical Logic by Ayush Upadhyaya Loyal (9k points) | 3.2k views

0 votes

3 answers

15

NET nov-17 paper-2 Q8
Let P and Q be two propositions , ~(P<->Q) is equivalent to : a)P<->~Q b)~P<->Q c)~P<->~Q d)Q->P

answered 5 days ago in Combinatory by Ammu9682 (25 points) | 318 views

+22 votes

5 answers

16

GATE2008-IT-21
Which of the following first order formulae is logically valid? Here $\alpha(x)$ is a first order formula with $x$ as a free variable, and $\beta$ is a first order formula with no free variable. $[\beta \rightarrow (\exists x, \alpha(x))] \rightarrow [\forall x, ... ) \rightarrow \beta]$ $[(\forall x, \alpha(x)) \rightarrow \beta] \rightarrow [\forall x, \alpha(x) \rightarrow \beta]$

answered 5 days ago in Mathematical Logic by Ayush Upadhyaya Loyal (9k points) | 2.4k views

0 votes

0 answers

17

Infinite Descending Chain
From Wiki :- Given a set S with a partial order ≤, an infinite descending chain is an infinite, strictly decreasing sequence of elements x1 > x2 > ... > xn > ... As an example, in the set of integers, the chain −1, ... used in number theory, while the latter is preferred in set theory and computer science. Now while solving question which definition to use ?

asked 5 days ago in Set Theory & Algebra by Na462 Active (3.3k points) | 8 views

0 votes

0 answers

18

self doubt
number of integers in the set {0,1,2,3......,10000}which contain digit 5 exactly once ???? i got the 9*9*9*9 is it right???

asked 5 days ago in Combinatory by vijju532 (97 points) | 27 views

+7 votes

1 answer

19

ISI2017 MMA
Let S ⊆ R. Consider the statement: "There exists a continuous function f:S -> S such that f(x) != x for all x belongs to S." This statement is false if S equals A) [2,3] B) (2,3] c) [-3,-2] union [2,3] D) (-infinity to +infinity ... -infinity to +infinity, f(x) will definitely be equal to x at some point but we want this to not happen as said in the question. Am I correct?

answered 6 days ago in Set Theory & Algebra by Kushagra Chatterjee Loyal (8.2k points) | 284 views

0 votes

1 answer

20

spanning tree
How we get maximum no. of spanning tree for give $n$ node is $n^{(n-2)}$

answered 6 days ago in Graph Theory by Anil Ji Active (1.5k points) | 19 views

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0 answers

21

Kenneth rosen
How many non-isomorphic directed graphs are there with $n$ vertices when $n$ is $2$ $3$ $4$

asked 6 days ago in Graph Theory by swati96 (37 points) | 17 views

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0 answers

22

Kenneth rosen
How many non-isomorphic graphs are there with six vertices and four edges?

asked 6 days ago in Graph Theory by swati96 (37 points) | 5 views

0 votes

0 answers

23

Graphs, kenneth rosen
How many non-isomorphic simple graphs are there with five vertices and three edges?

asked 6 days ago in Graph Theory by swati96 (37 points) | 7 views

0 votes

0 answers

24

Graphs, kenneth rosen
How many non-isomorphic simple graphs are there with five vertices and three edges? [closed]

asked 6 days ago in Graph Theory by swati96 (37 points) | 5 views

+26 votes

6 answers

25

GATE2017-1-02
Consider the first-order logic sentence $F:\forall x(\exists yR(x,y))$. Assuming non-empty logical domains, which of the sentences below are implied by $F$? $\exists y(\exists xR(x,y))$ $\exists y(\forall xR(x,y))$ $\forall y(\exists xR(x,y))$ $¬\exists x(\forall y¬R(x,y))$ IV only I and IV only II only II and III only

answered 6 days ago in Mathematical Logic by Ayush Upadhyaya Loyal (9k points) | 3.5k views

+1 vote

2 answers

26

planar graphs
Is there any subgraph homoemorphic to K5 present in G1 for the following question? Which one of the following graphs is NOT planar? (A) G1 (B) G2 (C) G3 (D) G4 In this question planar drawings( no 2 edges intersect) for G2, G3 and G4 exists, thats why ... 't find any subgraph homoemorphic to K5 in G1 as a graph is non planar iff it contains a subgraph homoemorphic to K5 or K3,3...

answered Jun 17 in Graph Theory by Prashank (55 points) | 309 views

+25 votes

9 answers

27

GATE2014-1-49
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 $2-$pennants is ${( ... ), (1,2)}$. Note that the pennant $(1,2)$ is not the same as the pennant $(2,1)$. The number of $10-$pennants is________

answered Jun 17 in Combinatory by Kumar Ashish Junior (545 points) | 1.8k views

0 votes

2 answers

28

self doubt
What is the English of both statement ∀x((x!=0)→∃y(xy=100)) ∀x∃y((x!=0)→(xy=100))

answered Jun 16 in Mathematical Logic by Deepakk Poonia (Dee) Boss (13.2k points) | 32 views

+2 votes

3 answers

29

UGCNET-Dec2014-III-57
The resolvent of the set of clauses $(A \vee B, \sim A \vee D, C \vee \sim B)$ is $A \vee B$ $C \vee D$ $A \vee C$ $A \vee D$

answered Jun 16 in Mathematical Logic by Prasanjeet Ghosh Active (1.3k points) | 578 views

+2 votes

3 answers

30

UGCNET-Dec2014-III-55
Equivalent logical expression for the Well Formed Formula $(WFF)$, $\sim(\forall x) F\left[x\right]$ is $\forall x (\sim F\left[x\right])$ $\sim (\exists x) F\left[x\right]$ $\exists x (\sim F\left[x\right])$ $\forall x F\left[x\right]$

answered Jun 16 in Mathematical Logic by Prasanjeet Ghosh Active (1.3k points) | 432 views

+2 votes

1 answer

31

Random_Doubt
if it is given -> "Every satisfiable propositional formula is not tautology" then what will it corresponds to? i am writing its hindi, which among below two are correct? "har ek satisfiable formula tautology nahi hota hai" // it is indeed truth. "koi bhi satisfiable formula hua, to wo tautology nahii hoga" // this is false.

answered Jun 16 in Mathematical Logic by Vegeta (21 points) | 33 views

0 votes

2 answers

32

IIT M video questions
P(x,y,z), xy=z, Universe is interger; write in logic form If xy=x for all y, then x =0. Thank you

answered Jun 14 in Mathematical Logic by Deepakk Poonia (Dee) Boss (13.2k points) | 51 views

0 votes

1 answer

33

self doubt
dog(x) = x is a dog Int (x) = x is intelligent write in logic form No dogs are intelligent.

answered Jun 14 in Mathematical Logic by Deepakk Poonia (Dee) Boss (13.2k points) | 31 views

0 votes

0 answers

34

generating funtion
1/1−2x2 provide close formula for the sequences it determines

asked Jun 14 in Mathematical Logic by sunil sarode Active (1.1k points) | 14 views

0 votes

2 answers

35

UGC NET DEC 2012 PAPER II Q-4
4. The power set of the set {ϕ} is (A) {ϕ} (B) {ϕ, {ϕ}} (C) {0} (D) {0, ϕ, {ϕ}}

answered Jun 14 in Set Theory & Algebra by Rajandeep Gill (23 points) | 186 views

0 votes

0 answers

36

Abstract algebra question
What is the maximal order of an element in S7? The symbol Sn will stand for the set of all permutations of the symbols {1,2,···,n}, which is a group under composition.

asked Jun 13 in Set Theory & Algebra by Forrest Gump (47 points) | 10 views

0 votes

0 answers

37

discrete maths
P: Good mobile phones are not cheap Q: Cheap mobile phones are not good L: P implies Q M: Q implies P N: P is equivalent to Q Which one of the following about L, M, and N is CORRECT? (A) Only L is TRUE. (B) Only M is TRUE. (C) Only N is TRUE. (D) L, M and N are TRUE [closed]

asked Jun 13 in Mathematical Logic by Preety singhal (15 points) | 18 views

+1 vote

1 answer

38

Gateoverflow pdf

answered Jun 13 in Mathematical Logic by Aarzoo Chourasia (11 points) | 271 views

0 votes

0 answers

39

Logic-Kenneth Rosen (Ex1.4-11f)
Let S(x) be the predicate that "x is a student", F(x) be the predicate "x is a faculty member", and A(x,y) the predicate "x has asked y a question", where the domain consists of all people associated with your school. ... A(x,y) ) ) Doubt 2: What is the difference between my answer and rosen's answer.Which one is correct. Please help. [closed]

asked Jun 12 in Mathematical Logic by Ayush Upadhyaya Loyal (9k points) | 36 views

0 votes

0 answers

40

ISI 2014 MMA- 9

asked Jun 12 in Mathematical Logic by Sammohan Ganguly (417 points) | 21 views

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title	title:apple
content	content:apple
exclude	-tag:apple
force match	+apple
views	views:100
score	score:10
answers	answers:2
is accepted	isaccepted:true
is closed	isclosed:true

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