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total number of spanning tree
[closed]
asked
Jun 10
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Mathematical Logic
by
Sanjay Sharma
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GATE199525b
Determine the number of positive integers $(\leq 720)$ which are not divisible by any of $2,3$ or $5.$
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Jun 6
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Set Theory & Algebra
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Arjun
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gate1995
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#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 ${\Big[\frac{2^{n+1} + (1)^n}{3}\Big]}^2$ $(n+1)^2$ $(n1)^3$ $(n1)^2$
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Jun 5
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Combinatory
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`JEET
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57
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discretemathematics
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recurrence
#recurrencerelations
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4
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?
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Jun 4
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Mathematical Logic
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srestha
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66
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discretemathematics
mathematicallogic
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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
in
Set Theory & Algebra
by
srestha
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21
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discretemathematics
settheory&algebra
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1
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6
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
in
Mathematical Logic
by
srestha
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111k
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25
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discretemathematics
mathematicallogic
0
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0
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7
#Rosen exercise1 ,question71 counting
use mathematical induction to prove the sum rule for m tasks from the sum rule for two tasks.
asked
May 31
in
Combinatory
by
sandeep singh gaur
(
243
points)

21
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counting
+1
vote
1
answer
8
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
in
Mathematical Logic
by
srestha
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111k
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53
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mathematicallogic
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9
Descrete Mathematic ACE Text Book Practice Question #16
A women's health clinic has four doctors and each patient is assigned to one of them. If a patient givs birth btween 8 am and 4 pm, then her chance of being attended by her assigned doctor is 3/4, otherwise it is 1/4. What is the probability that ... is attended by the assigned doctor when she gives birth? (A) 25/144 (B) 5/12 (C) 7/12 (D) 1/12
[closed]
asked
May 30
in
Mathematical Logic
by
JAYKISHAN
(
83
points)

46
views
probability
acebooklet
0
votes
1
answer
10
Proposition Logic Question
Are these propositions? 1.This sentence is true 2.This sentence is false Aren’t these liar paradox?
asked
May 30
in
Mathematical Logic
by
Reshu $ingh
(
253
points)

89
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mathematicallogic
propositionallogic
discretemathematics
0
votes
0
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11
Ace booklet functions page:152 q.no 44
Let A, B, C are k element sets and let S be an n element set where k<=n. How many triples of functions f:A>S, g:B>S, h:C>S are there such that f, g and h are all injective and f(A) =g(B) =h(C) =?
asked
May 27
in
Set Theory & Algebra
by
chandan2teja
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75
points)

15
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+2
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2
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12
ACE ACADEMY BOOKLET QUESTION
Let $G$ $=$ $(V, E)$ be a simple nonempty connected undirected graph, in which every vertex has degree 4. For any partition $V$ into two nonempty and nonoverlapping subsets $S$ and $T$. Which of the following is true? There are at least two edges that ... $S$ and one end point in $T$ There are exactly one edge that have one end point in $S$ and one end point in $T$
asked
May 26
in
Graph Theory
by
`JEET
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66
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13
Ace academy booklet #graph theory
Which of the following is $\textbf{not}$ TRUE? (a) In a complete graph $K_n$ ($n$ $\geq$ $3$), Euler circuit exists $\Leftrightarrow$ $n$ is odd. (b) In a complete bipartite graph $K_{m,n}$ (m $\geq$ 2 and n $\geq$2), Euler circuit exists ... Euler circuit exits for all $n$ (d) In a wheel graph $W_n$ ($n \geq 4$), Euler circuit exits $\Leftrightarrow$ $n$ is even.
asked
May 26
in
Graph Theory
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`JEET
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34
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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
in
Graph Theory
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`JEET
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23
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graphtheory
discretemathematics
+1
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1
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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
in
Graph Theory
by
`JEET
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21
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discretemathematics
graphtheory
0
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16
Ace workbook lattice concept
If X is minimum element of S then X is related to y for all y belongs to S. Let [S;R] be a poset. If every non empty subset of S has a minimum element then a) S is Totally ordered set b) S is bounded set. C) S is complemented ... then 1 will be part of every non empty subset of S. Is this correct way of interpreting the question. If not can you please elaborate it
asked
May 26
in
Set Theory & Algebra
by
chandan2teja
(
75
points)

17
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0
votes
0
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17
Self DoubtLA
In a nonhomogeneous equation Ax = b, x has a unique solution when $A^{1}$ exists i.e x = $A^{1}$b but when det(A) = 0 then we have infinite solution or many solution. please give a mathematical explanation of how the 2nd statement occurs?
asked
May 26
in
Mathematical Logic
by
MRINMOY_HALDER
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1.2k
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30
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linearalgebra
systemofequations
0
votes
2
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18
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
in
Combinatory
by
srestha
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111k
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58
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discretemathematics
permutationsandcombinations
0
votes
2
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19
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
in
Combinatory
by
aditi19
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3.7k
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62
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discretemathematics
kennethrosen
inclusionexclusion
0
votes
0
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20
Hasse Doubt
what is the least upper bound of {a, b, c}?
asked
May 23
in
Set Theory & Algebra
by
aditi19
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3.7k
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40
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hassediagram
settheory&algebra
lattice
partialorder
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vote
1
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21
Made easy Test Series:Graph Theory+Automata
Consider a graph $G$ with $2^{n}$ vertices where the level of each vertex is a $n$ bit binary string represented as $a_{0},a_{1},a_{2},.............,a_{n1}$, where each $a_{i}$ is $0$ or $1$ ... and $y$ denote the degree of a vertex $G$ and number of connected component of $G$ for $n=8.$ The value of $x+10y$ is_____________
asked
May 23
in
Graph Theory
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srestha
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111k
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67
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madeeasytestseries
graphtheory
theoryofcomputation
+2
votes
0
answers
22
IISc CSA  Research Interview Question
Prove that the rank of the Adjacency Matrix which is associated with a $k$ regular graph is $k.$
asked
May 22
in
Graph Theory
by
ankitgupta.1729
Boss
(
13.2k
points)

68
views
graphtheory
linearalgebra
0
votes
1
answer
23
Made Easy Test Series:Lattice
The number of totally ordered set compatible to the given POSET are __________
asked
May 20
in
Set Theory & Algebra
by
srestha
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111k
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50
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madeeasytestseries
lattice
0
votes
1
answer
24
Discrete mathematics #TEST_BOOK
I Have doubt about the language. Is it asking about the sum of elements if we make the GBL set for the given lattice .
asked
May 20
in
Set Theory & Algebra
by
Shawn Frost
(
31
points)

28
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#discrete
#lattice
+2
votes
2
answers
25
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
in
Graph Theory
by
Hirak
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3k
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100
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graphtheory
discretemathematics
0
votes
2
answers
26
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
in
Set Theory & Algebra
by
srestha
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111k
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53
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poset
madeeasytestseries
discretemathematics
+1
vote
0
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27
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
in
Mathematical Logic
by
srestha
Veteran
(
111k
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35
views
discretemathematics
mathematicallogic
firstorderlogic
0
votes
0
answers
28
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
in
Set Theory & Algebra
by
souren
(
37
points)

36
views
discretemathematics
settheory&algebra
kennethrosen
0
votes
1
answer
29
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
in
Combinatory
by
aditi19
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3.7k
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36
views
relations
recurrence
recurrenceeqation
discretemathematics
combinational
0
votes
0
answers
30
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
in
Combinatory
by
aditi19
Active
(
3.7k
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32
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kennethrosen
discretemathematics
#recurrencerelations
recurrence
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