Recent questions in Discrete Mathematics

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1

total number of spanning tree
[closed]

asked Jun 10 in Mathematical Logic by Sanjay Sharma Boss (47.1k points) | 41 views

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1 answer

2

GATE1995-25b
Determine the number of positive integers $(\leq 720)$ which are not divisible by any of $2,3$ or $5.$

asked Jun 6 in Set Theory & Algebra by Arjun Veteran (406k points) | 60 views

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3

#ACE ACADEMY BOOKLET QUESTION
The solution of $\sqrt{a_n} – 2\sqrt{a_{n-1}} + \sqrt{a_{n-2}} = 0$ where $a_0 = 1$ and $a_1 = 2$ is ${\Big[\frac{2^{n+1} + (-1)^n}{3}\Big]}^2$ $(n+1)^2$ $(n-1)^3$ $(n-1)^2$

asked Jun 5 in Combinatory by `JEET Active (3.3k points) | 57 views

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1 answer

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?

asked Jun 4 in Mathematical Logic by srestha Veteran (111k points) | 66 views

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5

Doubt on a math question
Chk this question https://gateoverflow.in/100202/test-series-counting $1)$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 $\sum_{I=0}^{n}\left ( _{i}^{n}\textrm{C} \right ).2^{n-i}=3^{n}$??

asked Jun 4 in Set Theory & Algebra by srestha Veteran (111k points) | 21 views

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1 answer

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 Veteran (111k points) | 25 views

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7

#Rosen exercise-1 ,question-71 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 views

+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 Veteran (111k points) | 53 views

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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

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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 views

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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 (75 points) | 15 views

+2 votes

2 answers

12

ACE ACADEMY BOOKLET QUESTION
Let $G$ $=$ $(V, E)$ be a simple non-empty connected undirected graph, in which every vertex has degree 4. For any partition $V$ into two non-empty and non-overlapping 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 Active (3.3k points) | 66 views

+1 vote

3 answers

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 by `JEET Active (3.3k points) | 34 views

+1 vote

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 in Graph Theory by `JEET Active (3.3k points) | 23 views

+1 vote

1 answer

15

#ACE_ACADEMY_DISCRETE_MATHS_BOOKLET.
Which of the following is not true? (a) Number of edge-disjoint 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 Active (3.3k points) | 21 views

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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 views

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17

Self Doubt-LA
In a non-homogeneous 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 Active (1.2k points) | 30 views

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2 answers

18

Self Doubt-Combinatory
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 Veteran (111k points) | 58 views

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2 answers

19

Rosen 7e Exercise-8.5 Question-15 page no-558 Inclusion-Exclusion
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 Active (3.7k points) | 62 views

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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 Active (3.7k points) | 40 views

+1 vote

1 answer

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 $a_{0},a_{1},a_{2},.............,a_{n-1}$, 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 by srestha Veteran (111k points) | 67 views

+2 votes

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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

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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 Veteran (111k points) | 50 views

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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 views

+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 Active (3k points) | 100 views

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2 answers

26

Made Easy Test Series:Discrete Mathematics-Poset
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 Veteran (111k points) | 53 views

+1 vote

0 answers

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 points) | 35 views

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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

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1 answer

29

Recurrence Relation Self-Doubt
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 Active (3.7k points) | 36 views

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30

Rosen 7e Exercise 8.2 Questionno-26 page no-525 Recurrence Relation
What is the general form of the particular solution guaranteed to exist of the linear nonhomogeneous recurrence relation $a_n$=$6a_{n-1}$-$12a_{n-2}$+$8a_{n-3}$+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 points) | 32 views

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