Recent questions in Discrete Mathematics

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1

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).

asked 21 hours ago in Combinatory by Ayush Upadhyaya Loyal (9k points) | 11 views

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2 answers

2

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.

asked 21 hours ago in Combinatory by Ayush Upadhyaya Loyal (9k points) | 47 views

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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) | 45 views

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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?

asked 1 day ago in Combinatory by Ayush Upadhyaya Loyal (9k points) | 25 views

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5

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

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1 answer

6

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?

asked 3 days ago in Combinatory by Ayush Upadhyaya Loyal (9k points) | 28 views

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7

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.

asked 3 days ago in Mathematical Logic by bts (107 points) | 21 views

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8

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

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9

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

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10

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

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11

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

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12

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

asked Jun 18 in Graph Theory by swati96 (37 points) | 17 views

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13

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

asked Jun 18 in Graph Theory by swati96 (37 points) | 5 views

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0 answers

14

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

asked Jun 18 in Graph Theory by swati96 (37 points) | 7 views

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0 answers

15

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

asked Jun 18 in Graph Theory by swati96 (37 points) | 5 views

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1 answer

16

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

asked Jun 18 in Graph Theory by piya (99 points) | 19 views

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2 answers

17

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

asked Jun 16 in Mathematical Logic by Vegeta (21 points) | 32 views

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1 answer

18

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

asked Jun 14 in Mathematical Logic by Vegeta (21 points) | 31 views

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2 answers

19

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

asked Jun 14 in Mathematical Logic by Vegeta (21 points) | 51 views

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20

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

asked Jun 14 in Mathematical Logic by sunil sarode Active (1.2k points) | 14 views

+3 votes

1 answer

21

find close form of generating function discrete mathematics kenneth rosen

asked Jun 14 in Mathematical Logic by sunil sarode Active (1.2k points) | 56 views

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22

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

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23

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

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24

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

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0 answers

25

ISI 2014 MMA- 9

asked Jun 12 in Mathematical Logic by Sammohan Ganguly (417 points) | 22 views

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26

ISI 2014 MMA - 3

asked Jun 12 in Mathematical Logic by Sammohan Ganguly (417 points) | 24 views

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1 answer

27

ACE booklet
Please solv

asked Jun 12 in Set Theory & Algebra by Pradeep A (37 points) | 41 views

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0 answers

28

ACE booklet
Please solve this

asked Jun 12 in Set Theory & Algebra by Pradeep A (37 points) | 58 views

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0 answers

29

self doubt on previous year question
https://gateoverflow.in/8281/gate2015-1-34 what is the exact probablity ? nd is question is saying to have a tuple in which atleast there should be one element who has only one complement to satisfy the given property?

asked Jun 11 in Set Theory & Algebra by eyeamgj Active (2.4k points) | 15 views

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1 answer

30

ACE booklet
R be a set of real # and ( R, *) is a group with respect to operation a*b= a+b+2, then inverse of 2 is...... (a) -2 (b) -4 (c) -6 (d) -8

asked Jun 11 in Set Theory & Algebra by Pradeep A (37 points) | 20 views

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