Recent questions and answers in Discrete Mathematics

0 votes

1 answer

1

Doubt in P->Q->R
Which one is equivalent to p->q->r ? A) (p->q)->r B) p->(q->r) Plz give answer with proper explaination.

answered 4 hours ago in Mathematical Logic by Verma Ashish Junior (609 points) | 6 views

0 votes

1 answer

2

Group theory
How to solve it? Better solution

answered 8 hours ago in Mathematical Logic by Tesla! Boss (16.3k points) | 17 views

0 votes

2 answers

3

Proper edge coloring
What is the minimal number K such that there exists a proper edge coloring of the complete graph on 8 vertices with K colors? A) 28 B) 8 C) 7 D) 15

answered 8 hours ago in Graph Theory by Rishav Kumar Singh Active (2.8k points) | 59 views

0 votes

1 answer

4

Self doubt
Let (g,*) be a group of order p where p is a prime number then number of proper subgroup is? I am getting 1 that is identity element, but somewhere I read, it will be 0. Who is wrong?

answered 8 hours ago in Set Theory & Algebra by Tesla! Boss (16.3k points) | 12 views

0 votes

0 answers

5

Group theory
In theorem 1: It is said that group is abelian if and only if order of group is prime number In theorem 2 : It is said that the group having order as square of prime number is abelian Theorem 1: https://yutsumura.com/a-simple-abelian-group-if-and-only-if-the- ... The group is not abelian as order is not prime. Theorem 2: 4 = (2)^2 square of prime number hence abelian. Please clarify ..

asked 12 hours ago in Set Theory & Algebra by jatin khachane 1 (349 points) | 12 views

+12 votes

4 answers

6

GATE2008-IT-28
Consider the following Hasse diagrams. Which all of the above represent a lattice? (i) and (iv) only (ii) and (iii) only (iii) only (i), (ii) and (iv) only

answered 23 hours ago in Set Theory & Algebra by sutanay3 Active (2.2k points) | 2.2k views

0 votes

1 answer

7

Sir i am first year ug student plese help me what to concentrate for gate from 1st year

answered 1 day ago in Mathematical Logic by hitendra singh (219 points) | 23 views

0 votes

2 answers

8

Sets and relations
If A is a set of positive odd elements less than 10. Then what is the cardinality of set A?

answered 1 day ago in Set Theory & Algebra by aditi19 (261 points) | 68 views

0 votes

1 answer

9

Propositional Logic
Ans. A

answered 1 day ago in Mathematical Logic by imnitish Junior (671 points) | 13 views

0 votes

1 answer

10

self doubt
What will be lower bound of {g}

answered 1 day ago in Set Theory & Algebra by aditi19 (261 points) | 10 views

+5 votes

2 answers

11

ISI2004-MIII
The equation $\frac{1}{3}+\frac{1}{2}s^{2}+\frac{1}{6}s^{3}=s$ has exactly three solution in $[0.1]$ exactly one solution in $[0,1]$ exactly two solution in $[0,1]$ no solution in $[0,1]$

answered 1 day ago in Set Theory & Algebra by sutanay3 Active (2.2k points) | 120 views

0 votes

1 answer

12

Types of Functions
A and B are finite sets True or False 1) F:A-->B is one to one then F is Onto , where |A| = |B| 2) F:A-->A is one to one then F is Onto , where F is function on same set

answered 1 day ago in Set Theory & Algebra by Rishav Kumar Singh Active (2.8k points) | 14 views

0 votes

1 answer

13

Combination with repetition allowed
Ans. 0

answered 1 day ago in Mathematical Logic by Vikas Verma Junior (993 points) | 26 views

0 votes

0 answers

14

Lattice
Ans. C

asked 1 day ago in Mathematical Logic by Na462 Active (4.6k points) | 13 views

0 votes

2 answers

15

Propositional Logic
Ans. B

answered 1 day ago in Mathematical Logic by arvin Active (3.6k points) | 17 views

+1 vote

1 answer

16

Combinations and Permutations
In how many ways can 12 different books be parceled into 4 packets so that 3 of the packets contain 3 books each and one of them two books atleast, if all the packets have the same destination?

answered 1 day ago in Combinatory by arvin Active (3.6k points) | 62 views

0 votes

0 answers

17

Countability and Well Ordering
Is there any relation between countability and well ordering? I mean if a set is well ordered, does it have any influence on it being countable and vice versa?

asked 1 day ago in Set Theory & Algebra by Lakshay Kakkar Junior (987 points) | 6 views

0 votes

1 answer

18

Nested quantifiers
Let domain be set of all fruits. Represent the following English statement into logic. 1)There are exactly 2 apple. S1:∃x∃y[A(x)⋀A(y)⋀(x≠y)⋀∀z(A(z)→(x=z⋁y=z)] S2: ∃x∃y[A(x)⋀A(y)⋀x≠y]⋀~∃x∃y∃z[A(x)⋀A(y)∧A(z)⋀x≠y∧y≠z⋀z≠x] where A(m)= m is an apple Is S1↔S2 ? If yes then how can u convert S2 into S1 using negating quantifier predicates

answered 2 days ago in Mathematical Logic by arvin Active (3.6k points) | 12 views

0 votes

0 answers

19

Eigen vector

asked 2 days ago in Mathematical Logic by Shivangi Parashar 2 (41 points) | 11 views

0 votes

0 answers

20

Eigen vector

asked 3 days ago in Mathematical Logic by Shivangi Parashar 2 (41 points) | 15 views

+2 votes

2 answers

21

Permutations with restrictions
$Z =\left \{ {A,B,C,D,E,F,G} \right \}$ How many permutations of all elements of set $Z$ are possible when A cannot appear after D and C cannot appear after F C cannot appear after D

answered 3 days ago in Combinatory by aditi19 (261 points) | 64 views

0 votes

1 answer

22

Graph theory
In tree for every pair of vertices u!=v in G their is exactly 1 path from u to v .Please help me to prove this

answered 3 days ago in Graph Theory by goxul Active (1.1k points) | 23 views

0 votes

1 answer

23

State True/False
1. If f is bijective function then f-1 is also bijective function. 2. If f is surjective function then f-1 is a function but not surjective. 3. Inverse of a function 'f' is a function only when it is bijective. 4. If a relation R: X->Y is left total, then it must be a function.

answered 3 days ago in Set Theory & Algebra by shubham6596 (163 points) | 15 views

+1 vote

1 answer

24

TIFR-2011-Maths-A-22
There exists a group with a proper subgroup isomorphic to itself.

answered 3 days ago in Set Theory & Algebra by ami (23 points) | 76 views

0 votes

0 answers

25

Kenneth Rosen: Algeraic structure
https://gateoverflow.in/?qa=blob&qa_blobid=8621402344393100507 I am not able to understand How both structure have same signature? Two algebras are of same signature if they have same number of operations and same number of constants and also corresponding operations are of same arity.

asked 3 days ago in Mathematical Logic by Sandy Sharma Junior (693 points) | 6 views

0 votes

0 answers

26

Combinatorics
There are 100 students. 85 choose Math, 80 choose Physics, 75 choose Chemistry, 70 choose Biology. What is the minimum number of students choosing all 4 subjects? Assume each student chosen at least one subject?

asked 4 days ago in Combinatory by aditi19 (261 points) | 16 views

0 votes

0 answers

27

Relations and lattice
1. Every complemented lattice is distributed 2. Every Distributed lattice is complemented 3.Every Distributive lattice is bounded 4 .Every complemented lattice is bounded True or false

asked 4 days ago in Mathematical Logic by jatin khachane 1 (349 points) | 8 views

0 votes

2 answers

28

Boolean algebra theorem(Lattices)
THEOREM:- The Poset $[D_{n};/] $ is a boolean algebra iff 'n' is a square-free number. If the Poset $[D_{n};/] $ is a boolean algebra then compliment of $x = \frac{n}{x} \forall x\epsilon D_{n}$ Please explain this theorem?? and following question Q)Which of the following is not a ... A) [ D_{110};/ ] $ $ B) [ D_{91};/ ] $ $ C) [ D_{45};/ ]$ $ D) [ D_{64};/ ]$

answered 4 days ago in Set Theory & Algebra by K_Nishant (75 points) | 153 views

+11 votes

3 answers

29

GATE2008-23
Which of the following statements is true for every planar graph on $n$ vertices? The graph is connected The graph is Eulerian The graph has a vertex-cover of size at most $\frac{3n}{4}$ The graph has an independent set of size at least $\frac{n}{3}$

answered 4 days ago in Graph Theory by Pratik Gawali (107 points) | 1.7k views

+1 vote

1 answer

30

Rosen book Generating Functions pg no 430

answered 5 days ago in Combinatory by shubham6596 (163 points) | 19 views

0 votes

0 answers

31

GATE-2018-ECE
Let M be a real 4 × 4 matrix. Consider the following statements : S1 : M has 4 linearly independent eigenvectors. S2 : M has 4 distinct eigenvalues. S3 : M is non-singular (invertible). Whict one among the following is TRUE? (a) S1 implies S2 (b) S2 implies S1 (c) S1 implies S3 (d) S3 implies S2 Note: Plz explain in detail why other options are incorrect.

asked 5 days ago in Set Theory & Algebra by Manish11102 (31 points) | 9 views

0 votes

1 answer

32

Rosen Ch9.6
Determine whether each of these posets is well-ordered. (Q ∩[0, 1], ≤) (the set of rational numbers between 0 and 1 inclusive) The answer is not well ordered because as it doesn't have any unique least element as 0 can be expressed in p/q forms like (0/12,0/23,0/234). All are representing zero but there is no unique among them. Is this the reason here? Please confirm

answered 5 days ago in Set Theory & Algebra by rajatmyname Junior (969 points) | 12 views

+1 vote

0 answers

33

Descrete math
Which of the following is true ?

asked 5 days ago in Mathematical Logic by Prince Sindhiya Active (2.3k points) | 49 views

0 votes

1 answer

34

me test
A simple graph with n vertices is constructed by randomly and independently placing an edge between every two vertices with probability p. What is the expected no. of nodes with degree 2?

answered 6 days ago in Graph Theory by MansiS (83 points) | 33 views

+1 vote

3 answers

35

made easy test series
What is the number of partition of X={a,b,c,d,e,f}.where 'a' and 'c' are always in same block?

answered 6 days ago in Mathematical Logic by Vikas Verma Junior (993 points) | 74 views

0 votes

1 answer

36

made easy test series
Consider F be a family of all subsets of set {1,2,3,.....100} that contain atleast 50 numbers,partially ordered with respect to containment.Then maximum size of chains in the poset (F,⊆) that cover F is

answered 6 days ago in Mathematical Logic by gauravkc Loyal (6.1k points) | 23 views

+1 vote

2 answers

37

Graph theory Modified
What is the maximum integer value m such that every simple connected graph with r vertices and r+2 edges contains at least m different spanning trees ? 1)1 2)4 3)8 4)m

answered 6 days ago in Graph Theory by Surajit13 (11 points) | 132 views

+1 vote

1 answer

38

Sets ,DM
Let P ( S ) denotes the power set of the set S, the dual of the lattice ( P(S), ⊆ ) is a) Doesn't’t exist b) ( P(S), ⊆ ) c) ( P(S), ⊇ ) d) ( S,⊇)

answered 6 days ago in Mathematical Logic by arvin Active (3.6k points) | 20 views

+3 votes

2 answers

39

How many maximum cycles possible in any Complete graph? (Unlabelled nodes)

answered Aug 14 in Graph Theory by K_Nishant (75 points) | 231 views

+4 votes

2 answers

40

Number of Hamiltonian cycles in a complete graph

answered Aug 13 in Graph Theory by K_Nishant (75 points) | 350 views

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