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Recent questions and answers in Discrete Mathematics
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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.
answered
13 hours
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Combinatory
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srestha
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86.9k
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47
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discretemathematics
kennethrosen
permutationsandcombinations
0
votes
1
answer
2
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).
answered
18 hours
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Combinatory
by
Anu007
Boss
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11
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discretemathematics
permutationsandcombinations
0
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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.
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1 day
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Combinatory
by
Ayush Upadhyaya
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9k
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44
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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?
answered
1 day
ago
in
Combinatory
by
Soumya29
Loyal
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9.9k
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23
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kennethrosen
permutationsandcombinations
+1
vote
2
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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
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Graph Theory
by
himanshu19
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691
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232
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graphconnectivity
+2
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1
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6
find close form of generating function discrete mathematics kenneth rosen
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Mathematical Logic
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neeraj33negi
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399
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53
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kennethrosen
discretemathematics
counting
+1
vote
2
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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
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Graph Theory
by
himanshu19
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691
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131
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discretemathematics
graphtheory
0
votes
0
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8
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
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Combinatory
by
Ayush Upadhyaya
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9k
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29
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discretemathematics
permutationsandcombinations
0
votes
1
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9
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?
answered
2 days
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Combinatory
by
Sumeet Singh
Junior
(
501
points)

28
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discretemathematics
permutationsandcombinations
+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
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Graph Theory
by
Prashank
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55
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105
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graphtheory
graphcoloring
0
votes
1
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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
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Mathematical Logic
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Shubhgupta
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669
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20
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rankofmatrix
engineeringmathematics
matrix
0
votes
0
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12
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)]
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4 days
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Mathematical Logic
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Roma_nagpal
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115
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20
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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?
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5 days
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Mathematical Logic
by
Pratyush
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7
points)

24
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+33
votes
7
answers
14
GATE2015324
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
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9k
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3.2k
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gate20153
mathematicallogic
difficult
logicalreasoning
0
votes
3
answers
15
NET nov17 paper2 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
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5 days
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in
Combinatory
by
Ammu9682
(
25
points)

318
views
+22
votes
5
answers
16
GATE2008IT21
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
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in
Mathematical Logic
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Ayush Upadhyaya
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9k
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2.4k
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gate2008it
firstorderlogic
normal
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 ?
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in
Set Theory & Algebra
by
Na462
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3.3k
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8
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discretemathematics
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
discretemathematics
+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
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284
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isi2017
functions
usermod
0
votes
1
answer
20
spanning tree
How we get maximum no. of spanning tree for give $n$ node is $n^{(n2)}$
answered
6 days
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Graph Theory
by
Anil Ji
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1.5k
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19
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engineeringmathematics
discretemathematics
graphtheory
0
votes
0
answers
21
Kenneth rosen
How many nonisomorphic 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
engineeringmathematics
discretemathematics
kennethrosen
graphtheory
0
votes
0
answers
22
Kenneth rosen
How many nonisomorphic graphs are there with six vertices and four edges?
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6 days
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in
Graph Theory
by
swati96
(
37
points)

5
views
engineeringmathematics
discretemathematics
graphtheory
0
votes
0
answers
23
Graphs, kenneth rosen
How many nonisomorphic simple graphs are there with five vertices and three edges?
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6 days
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in
Graph Theory
by
swati96
(
37
points)

7
views
engineeringmathematics
discretemathematics
kennethrosen
graphtheory
0
votes
0
answers
24
Graphs, kenneth rosen
How many nonisomorphic simple graphs are there with five vertices and three edges?
[closed]
asked
6 days
ago
in
Graph Theory
by
swati96
(
37
points)

5
views
engineeringmathematics
discretemathematics
graphtheory
+26
votes
6
answers
25
GATE2017102
Consider the firstorder logic sentence $F:\forall x(\exists yR(x,y))$. Assuming nonempty 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
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in
Mathematical Logic
by
Ayush Upadhyaya
Loyal
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9k
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3.5k
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gate20171
mathematicallogic
firstorderlogic
+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
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graphtheory
graphplanarity
+25
votes
9
answers
27
GATE2014149
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
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545
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1.8k
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gate20141
permutationsandcombinations
numericalanswers
normal
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
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32
views
+2
votes
3
answers
29
UGCNETDec2014III57
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
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578
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ugcnetdec2014iii
mathematicallogic
+2
votes
3
answers
30
UGCNETDec2014III55
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
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Prasanjeet Ghosh
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432
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ugcnetdec2014iii
mathematicallogic
+2
votes
1
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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
discretemathematics
propositionallogic
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
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Deepakk Poonia (Dee)
Boss
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13.2k
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51
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propositionallogic
firstorderlogic
logicalreasoning
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
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13.2k
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31
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propositionallogic
firstorderlogic
logicalreasoning
0
votes
0
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34
generating funtion
1/1−2x2 provide close formula for the sequences it determines
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Jun 14
in
Mathematical Logic
by
sunil sarode
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1.1k
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generatingfunctions
kennethrosen
discretemathematics
0
votes
2
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35
UGC NET DEC 2012 PAPER II Q4
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
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ugcnetdec2012ii
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
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10
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settheory&algebra
algebra
0
votes
0
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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
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Preety singhal
(
15
points)

18
views
+1
vote
1
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38
Gateoverflow pdf
answered
Jun 13
in
Mathematical Logic
by
Aarzoo Chourasia
(
11
points)

271
views
0
votes
0
answers
39
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
40
ISI 2014 MMA 9
asked
Jun 12
in
Mathematical Logic
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Sammohan Ganguly
(
417
points)

21
views
userisi2014
usermod
engineeringmathematics
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