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Recent questions in Discrete Mathematics
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CombinatoricsKenneth Rosen(Ex 5.341)
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
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(
9k
points)

11
views
discretemathematics
permutationsandcombinations
0
votes
2
answers
2
CombinatoricsKenneth 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
discretemathematics
kennethrosen
permutationsandcombinations
0
votes
0
answers
3
CombinatoricsKenneth 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
pigeonholeprinciple
discretemathematics
0
votes
1
answer
4
CombinatoricsKenneth 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
kennethrosen
permutationsandcombinations
0
votes
0
answers
5
CombinatoricsSelf 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
discretemathematics
permutationsandcombinations
0
votes
1
answer
6
CombinatoricsSelf 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
discretemathematics
permutationsandcombinations
0
votes
1
answer
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
rankofmatrix
engineeringmathematics
matrix
0
votes
0
answers
8
UGCNETNov2017III70
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
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
0
votes
0
answers
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 ?
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6 days
ago
in
Set Theory & Algebra
by
Na462
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3.3k
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8
views
discretemathematics
0
votes
0
answers
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
discretemathematics
0
votes
0
answers
12
Kenneth rosen
How many nonisomorphic 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
engineeringmathematics
discretemathematics
kennethrosen
graphtheory
0
votes
0
answers
13
Kenneth rosen
How many nonisomorphic graphs are there with six vertices and four edges?
asked
Jun 18
in
Graph Theory
by
swati96
(
37
points)

5
views
engineeringmathematics
discretemathematics
graphtheory
0
votes
0
answers
14
Graphs, kenneth rosen
How many nonisomorphic simple graphs are there with five vertices and three edges?
asked
Jun 18
in
Graph Theory
by
swati96
(
37
points)

7
views
engineeringmathematics
discretemathematics
kennethrosen
graphtheory
0
votes
0
answers
15
Graphs, kenneth rosen
How many nonisomorphic simple graphs are there with five vertices and three edges?
[closed]
asked
Jun 18
in
Graph Theory
by
swati96
(
37
points)

5
views
engineeringmathematics
discretemathematics
graphtheory
0
votes
1
answer
16
spanning tree
How we get maximum no. of spanning tree for give $n$ node is $n^{(n2)}$
asked
Jun 18
in
Graph Theory
by
piya
(
99
points)

19
views
engineeringmathematics
discretemathematics
graphtheory
0
votes
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
0
votes
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
propositionallogic
firstorderlogic
logicalreasoning
0
votes
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
propositionallogic
firstorderlogic
logicalreasoning
0
votes
0
answers
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
generatingfunctions
kennethrosen
discretemathematics
+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
kennethrosen
discretemathematics
counting
0
votes
0
answers
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
settheory&algebra
algebra
0
votes
0
answers
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
0
votes
0
answers
24
LogicKenneth Rosen (Ex1.411f)
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
discretemathematics
propositionallogic
0
votes
0
answers
25
ISI 2014 MMA 9
asked
Jun 12
in
Mathematical Logic
by
Sammohan Ganguly
(
417
points)

22
views
userisi2014
usermod
engineeringmathematics
0
votes
0
answers
26
ISI 2014 MMA  3
asked
Jun 12
in
Mathematical Logic
by
Sammohan Ganguly
(
417
points)

24
views
userisi2014
usermod
engineeringmathematics
0
votes
1
answer
27
ACE booklet
Please solv
asked
Jun 12
in
Set Theory & Algebra
by
Pradeep A
(
37
points)

41
views
0
votes
0
answers
28
ACE booklet
Please solve this
asked
Jun 12
in
Set Theory & Algebra
by
Pradeep A
(
37
points)

58
views
0
votes
0
answers
29
self doubt on previous year question
https://gateoverflow.in/8281/gate2015134 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
0
votes
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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