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Recent questions tagged discretemathematics
+2
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answer
1
ISRO202073
Given that $B(a)$ means “$a$ is a bear” $F(a)$ means “$a$ is a fish” and $E(a,b)$ means “$a $ eats $b$” Then what is the best meaning of $\forall x [F(x) \to \forall y(E(y,x)\rightarrow b(y))]$ Every fish is eaten by some bear Bears eat only fish Every bear eats fish Only bears eat fish
asked
Jan 13
in
Mathematical Logic
by
Satbir
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24.2k
points)

245
views
isro2020
discretemathematics
mathematicallogic
propositionallogic
normal
+1
vote
1
answer
2
ISRO202076
If $A=\{x,y,z\}$ and $B=\{u,v,w,x\}, $ and the universe is $\{s,t,u,v,w,x,y,z\}$ Then $(A \cup B’) \cap (A \cap B)$ is equal to $\{u,v,w,x\}$ $\{ \ \}$ $\{u,v,w,x,y,z\}$ $\{u,v,w\}$
asked
Jan 13
in
Set Theory & Algebra
by
Satbir
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24.2k
points)

141
views
isro2020
discretemathematics
settheory&algebra
sets
easy
0
votes
0
answers
3
Discrete mathematics 7th ed by Kenneth Rosen,chapter3:Algorithm
Should not there be a second condition stating i = j1 in While loop's conditional statement,if not then it seems to me while loop will be a infinite loop..
asked
Jun 12, 2019
in
Algorithms
by
souren
(
37
points)

107
views
discretemathematics
algorithms
sorting
0
votes
1
answer
4
Sheldon Ross Example5n
Compute the probability that if 10 married couples are seated at random at a round table, then no wife sits next to her husband 1 wife sits next to her husband. pick one of the 10 couples=$\binom{10}{1}$. These couples can interchange their position such that ... sits together=$\frac{N}{19!}$ so probability that no couple sits together=$1\frac{N}{19!}$ is this correct?
asked
Jun 11, 2019
in
Probability
by
aditi19
Loyal
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5.2k
points)

194
views
permutationandcombination
probability
discretemathematics
sheldonross
+1
vote
1
answer
5
#ACE ACADEMY BOOKLET QUESTION
The solution of $\sqrt{a_n} – 2\sqrt{a_{n1}} + \sqrt{a_{n2}} = 0$ where $a_0 = 1$ and $a_1 = 2$ is ${\Big[\frac{2^{n+1} + (1)^n}{3}\Big]}^2$ $(n+1)^2$ $(n1)^3$ $(n1)^2$
asked
Jun 5, 2019
in
Combinatory
by
`JEET
Boss
(
19.2k
points)

148
views
discretemathematics
permutationandcombination
recurrence
#recurrencerelations
+3
votes
1
answer
6
Mathematical Logic Ques:Self doubt
“Not every satisfiable logic is valid” Representation of it will be $1)\sim \left ( \forall S(x)\rightarrow V(x) \right )$ or $2)\sim \left ( \forall S(x)\vee V(x) \right )$ Among $1)$ and $2)$, which one is correct? and why?
asked
Jun 4, 2019
in
Mathematical Logic
by
srestha
Veteran
(
119k
points)

196
views
discretemathematics
mathematicallogic
0
votes
0
answers
7
Doubt on a math question
Chk this question https://gateoverflow.in/100202/testseriescounting $1)$Can someone verify this ans?? See if $\left ( _{0}^{6}\textrm{C} \right )$ in one set, other set will contain $\left ( _{6}^{6}\textrm{C} \right )$ elements. right?? Now why do we again need $2^{n}$ ... meaning of it?? $2)$ How $\sum_{I=0}^{n}\left ( _{i}^{n}\textrm{C} \right ).2^{ni}=3^{n}$??
asked
Jun 4, 2019
in
Set Theory & Algebra
by
srestha
Veteran
(
119k
points)

53
views
discretemathematics
settheory&algebra
0
votes
1
answer
8
GATE 2019:EC
The value of integral $\int_{0}^{\pi }\int_{y}^{\pi }\frac{\sin x}{x}dxdy$ is equal to_________
asked
Jun 2, 2019
in
Linear Algebra
by
srestha
Veteran
(
119k
points)

95
views
discretemathematics
0
votes
2
answers
9
GATE 2017:EC
Consider the $5\times 5$ matrix: $\begin{bmatrix} 1 & 2 &3 & 4 &5 \\ 5 &1 &2 & 3 &4 \\ 4& 5 &1 &2 &3 \\ 3& 4 & 5 & 1 &2 \\ 2&3 & 4 & 5 & 1 \end{bmatrix}$ It is given $A$ has only one real eigen value. Then the real eigen value of $A$ is ________
asked
Jun 2, 2019
in
Linear Algebra
by
srestha
Veteran
(
119k
points)

217
views
discretemathematics
linearalgebra
matrices
+2
votes
4
answers
10
GATE2017 EC
The rank of the matrix $\begin{bmatrix} 1 & 1 & 0 &0 & 0\\ 0 & 0 & 1 &1 &0 \\ 0 &1 &1 &0 &0 \\ 1 & 0 &0 & 0 &1 \\ 0&0 & 0 & 1 & 1 \end{bmatrix}$ is ________. Ans 5?
asked
Jun 1, 2019
in
Linear Algebra
by
srestha
Veteran
(
119k
points)

310
views
discretemathematics
matrices
+2
votes
1
answer
11
Doubt on GATE Question
Read the statements: All women are entrepreneurs. Some women are doctors. Which of the following conclusions can be logically inferred from the above statements? All women are doctors All doctors are entrepreneurs All entrepreneurs are women Some entrepreneurs are doctors ... Is it because , if we make set of doctor as 0, then All doctors are entrepreneurs is meaningless.
asked
Jun 1, 2019
in
Mathematical Logic
by
srestha
Veteran
(
119k
points)

75
views
discretemathematics
mathematicallogic
+1
vote
1
answer
12
Mathematical Logic: Doubt on meaning of statement
The notation $\exists ! x P(x)$ denotes the proposition there exists a unique $x$ such that $P(x)$ ... What will be answer here?? Is the assumption only for left hand side and not right hand side??
asked
May 31, 2019
in
Mathematical Logic
by
srestha
Veteran
(
119k
points)

100
views
mathematicallogic
discretemathematics
0
votes
1
answer
13
Proposition Logic Question
Are these propositions? 1.This sentence is true 2.This sentence is false Aren’t these liar paradox?
asked
May 30, 2019
in
Mathematical Logic
by
Reshu $ingh
(
265
points)

170
views
mathematicallogic
propositionallogic
discretemathematics
+2
votes
1
answer
14
ACE ACADEMY BOOKLET
Which of the following is $\textbf{not}$ TRUE? (a) In a complete graph $K_n$ ($n$ $\geq$ $3$), Hamiltonian cycle exists for all n. (b) In a complete bipartite graph $K_{m,n}$ (m $\geq$ 2 and n $\geq$2), Hamiltonian cycle exists $\Leftrightarrow$ ... Hamiltonian cycle exits for all $n$ (d) In a wheel graph $W_n$ ($n \geq 4$), Hamiltonian cycle exits $\Leftrightarrow$ $n$ is even.
asked
May 26, 2019
in
Graph Theory
by
`JEET
Boss
(
19.2k
points)

86
views
graphtheory
discretemathematics
+1
vote
2
answers
15
#ACE_ACADEMY_DISCRETE_MATHS_BOOKLET.
Which of the following is not true? (a) Number of edgedisjoint Hamiltonian cycles in $K_7$ is $3$ (b) If $G$ is a simple graph with $6$ vertices and the degree of each vertex is at least $3$, then the Hamiltonian cycle exists in ... simple graph with $5$ vertices and $7$ edges, then the Hamiltonian cycle exists in $G$ Please help me understand all the options.
asked
May 26, 2019
in
Graph Theory
by
`JEET
Boss
(
19.2k
points)

149
views
discretemathematics
graphtheory
0
votes
3
answers
16
Self DoubtCombinatory
In how many ways we can put $n$ distinct balls in $k$ dintinct bins?? Will it be $n^{k}$ or $k^{n}$?? Taking example will be easy way to remove this doubt or some other ways possible??
asked
May 25, 2019
in
Combinatory
by
srestha
Veteran
(
119k
points)

112
views
discretemathematics
permutationandcombination
0
votes
2
answers
17
Rosen 7e Exercise8.5 Question15 page no558 InclusionExclusion
How many permutations of the 10 digits either begin with the 3 digits 987, contain the digits 45 in the fifth and sixth positions, or end with the 3 digits 123?
asked
May 24, 2019
in
Combinatory
by
aditi19
Loyal
(
5.2k
points)

109
views
discretemathematics
kennethrosen
inclusionexclusion
+2
votes
2
answers
18
GateForum Question Bank :Graph Theory
What is the probability that there is an edge in an undirected random graph having 8 vertices? 1 1/8
asked
May 19, 2019
in
Graph Theory
by
Hirak
Active
(
3.6k
points)

161
views
graphtheory
discretemathematics
+1
vote
0
answers
19
Recurrence RelationSelf Doubt(Discrete Math+Algo)
Let $A(n)$ denotes the number of $n$ bit binary strings which have no pair of consecutive $1’s.$ what will be recurrence relation for it and what will be it’s Time Complexity??
asked
May 19, 2019
in
Algorithms
by
srestha
Veteran
(
119k
points)

79
views
discretemathematics
recurrenceeqation
algorithms
0
votes
2
answers
20
Made Easy Test Series:Discrete MathematicsPoset
Consider the following Posets: $I)\left ( \left \{ 1,2,5,7,10,14,35,70 \right \},\leq \right )$ $II)\left ( \left \{ 1,2,3,6,14,21,42 \right \},/ \right )$ $III)\left ( \left \{ 1,2,3,6,11,22,33,66 \right \},/ \right )$ Which of the above poset are isomorphic to $\left ( P\left ( S \right ),\subseteq \right )$ where $S=\left \{ a,b,c \right \}?$
asked
May 18, 2019
in
Set Theory & Algebra
by
srestha
Veteran
(
119k
points)

82
views
poset
madeeasytestseries
discretemathematics
+1
vote
0
answers
21
Self Doubt:Mathematical Logic
Represent these two statement in first order logic: $A)$ Only Alligators eat humans $B)$ Every Alligator eats humans Is Every represents $\equiv \exists$ and Only represents $\equiv \forall$ ?? Can we differentiate it with verb ‘eat’ and ‘eats’??
asked
May 18, 2019
in
Mathematical Logic
by
srestha
Veteran
(
119k
points)

73
views
discretemathematics
mathematicallogic
firstorderlogic
0
votes
0
answers
22
Discrete Mathematics by Kenneth Rosen,section2.4,recursive functions
$C_{a}^{k}:\mathbb{N}^{k}\rightarrow \mathbb{N}$ I am studying discrete math from beginnings and came across this term in primitive recursive function.I don't know what $C_{a}^{k}$ means and does $\mathbb{N}$ means set of natural numbers?Someone please help me out.
asked
May 15, 2019
in
Set Theory & Algebra
by
souren
(
37
points)

59
views
discretemathematics
settheory&algebra
kennethrosen
+1
vote
1
answer
23
Recurrence Relation SelfDoubt
What will be solution of recurrence relation if roots are like this: r1=2, r2=2, r3=2, r4=2 is this the case of repetitive roots?
asked
May 14, 2019
in
Combinatory
by
aditi19
Loyal
(
5.2k
points)

67
views
relations
recurrence
recurrenceeqation
discretemathematics
combinational
0
votes
0
answers
24
Rosen 7e Exercise 8.2 Questionno26 page no525 Recurrence Relation
What is the general form of the particular solution guaranteed to exist of the linear nonhomogeneous recurrence relation $a_n$=$6a_{n1}$$12a_{n2}$+$8a_{n3}$+F(n) if F(n)=$n^2$ F(n)=$2^n$ F(n)=$n2^n$ F(n)=$(2)^n$ F(n)=$n^22^n$ F(n)=$n^3(2)^n$ F(n)=3
asked
May 14, 2019
in
Combinatory
by
aditi19
Loyal
(
5.2k
points)

72
views
kennethrosen
discretemathematics
#recurrencerelations
recurrence
0
votes
0
answers
25
Rosen 7e Exercise8.2 Question no23 page no525 Recurrence Relation
Consider the nonhomogeneous linear recurrence relation $a_n$=$3a_{n1}$+$2^n$ in the book solution is given $a_n$=$2^{n+1}$ but I’m getting $a_n$=$3^{n+1}2^{n+1}$
asked
May 13, 2019
in
Combinatory
by
aditi19
Loyal
(
5.2k
points)

57
views
kennethrosen
discretemathematics
#recurrencerelations
recurrence
+1
vote
1
answer
26
ISI2018PCBCS3
An $n$variable Boolean function $f:\{0,1\}^n \rightarrow \{0,1\} $ is called symmetric if its value depends only on the number of $1’s$ in the input. Let $\sigma_n $ denote the number of such functions. Calculate the value of $\sigma_4$. Derive an expression for $\sigma_n$ in terms of $n$.
asked
May 12, 2019
in
Set Theory & Algebra
by
akash.dinkar12
Boss
(
42.5k
points)

45
views
isi2018pcbcs
engineeringmathematics
discretemathematics
settheory&algebra
functions
descriptive
+2
votes
1
answer
27
ISI2018MMA26
Let $C_i(i=0,1,2...n)$ be the coefficient of $x^i$ in $(1+x)^n$.Then $\frac{C_0}{2} – \frac{C_1}{3}+\frac{C_2}{4}\dots +(1)^n \frac{C_n}{n+2}$ is equal to $\frac{1}{n+1}\\$ $\frac{1}{n+2}\\$ $\frac{1}{n(n+1)}\\$ $\frac{1}{(n+1)(n+2)}$
asked
May 11, 2019
in
Combinatory
by
akash.dinkar12
Boss
(
42.5k
points)

163
views
isi2018mma
engineeringmathematics
discretemathematics
generatingfunctions
0
votes
1
answer
28
ISI2018MMA15
Let $G$ be a finite group of even order. Then which of the following statements is correct? The number of elements of order $2$ in $G$ is even The number of elements of order $2$ in $G$ is odd $G$ has no subgroup of order $2$ None of the above.
asked
May 11, 2019
in
Set Theory & Algebra
by
akash.dinkar12
Boss
(
42.5k
points)

96
views
isi2018mma
engineeringmathematics
discretemathematics
settheory&algebra
grouptheory
+1
vote
1
answer
29
ISI2018MMA10
A new flag of ISI club is to be designed with $5$ vertical strips using some or all of the four colors: green, maroon, red and yellow. In how many ways this can be done so that no two adjacent strips have the same color? $120$ $324$ $424$ $576$
asked
May 11, 2019
in
Combinatory
by
akash.dinkar12
Boss
(
42.5k
points)

64
views
isi2018mma
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
0
answers
30
Rosen 7e Exercise9.6 Question no27 page no631
What is the covering relation of the partial ordering {(A, B)  A ⊆ B} on the power set of S, where S = {a, b, c}? i'm getting R={(Ф, {a}), (Ф, {b}), (Ф, {c}), (Ф, {a, b}), (Ф, {b, c}), (Ф, {a, c}), (Ф, {a, b, c}), ({a}, {a, b}), ({a}, {a, c}), ({b}, ... b, c}), ({c}, {a, c}), ({c}, {b, c}), ({a, b}, {a, b, c}), ({a, c}, {a, b, c})({b, c}, {a, b, c})
asked
May 10, 2019
in
Set Theory & Algebra
by
aditi19
Loyal
(
5.2k
points)

74
views
kennethrosen
discretemathematics
relations
settheory&algebra
sets
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