Recent questions and answers in Discrete Mathematics

+18 votes

5 answers

1

GATE2000-1.1
The minimum number of cards to be dealt from an arbitrarily shuffled deck of $52$ cards to guarantee that three cards are from same suit is $3$ $8$ $9$ $12$

answered 21 hours ago in Combinatory by Asim Siddiqui 4 Active (1.2k points) | 2.9k views

+25 votes

4 answers

2

GATE2006-73
The $2^n$ vertices of a graph $G$ corresponds to all subsets of a set of size $n$, for $n \geq 6$. Two vertices of $G$ are adjacent if and only if the corresponding sets intersect in exactly two elements. The number of connected components in $G$ is: $n$ $n + 2$ $2^{\frac{n}{2}}$ $\frac{2^{n}}{n}$

answered 1 day ago in Graph Theory by shaktisingh (241 points) | 2.4k views

+38 votes

6 answers

3

GATE2005-44
What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two pairs $(a,b)$ and $(c,d)$ in the chosen set such that, $a \equiv c\mod 3$ and $b \equiv d \mod 5$ $4$ $6$ $16$ $24$

answered 3 days ago in Combinatory by techbd123 Active (1.4k points) | 4.2k views

+3 votes

2 answers

4

CMI2015-A-10
The school athletics coach has to choose 4 students for the relay team. He calculates that there are 3876 ways of choosing the team if the order in which the runners are placed is not considered. How many ways are there of choosing the team if the order of the ... taken into account? Between 12,000 and 25,000 Between 75,000 and 99,999 Between 30,000 and 60,000 More than 100,000

answered 3 days ago in Combinatory by chirudeepnamini Active (1.8k points) | 92 views

+21 votes

5 answers

5

GATE2018-27
Let $N$ be the set of natural numbers. Consider the following sets, $P:$ Set of Rational numbers (positive and negative) $Q:$ Set of functions from $\{0,1\}$ to $N$ $R:$ Set of functions from $N$ to $\{0, 1\}$ $S:$ Set of finite subsets of $N$ Which of the above sets are countable? $Q$ and $S$ only $P$ and $S$ only $P$ and $R$ only $P, Q$ and $S$ only

answered 4 days ago in Set Theory & Algebra by JashanArora Junior (827 points) | 4.6k views

+1 vote

2 answers

6

set theory

answered 4 days ago in Set Theory & Algebra by Spidey_guy (111 points) | 50 views

+50 votes

7 answers

7

GATE2016-2-28
Consider a set $U$ of $23$ different compounds in a chemistry lab. There is a subset $S$ of $U$ of $9$ compounds, each of which reacts with exactly $3$ compounds of $U$. Consider the following statements: Each compound in U \ S reacts with an odd number ... in U \ S reacts with an even number of compounds. Which one of the above statements is ALWAYS TRUE? Only I Only II Only III None.

answered 4 days ago in Set Theory & Algebra by Spidey_guy (111 points) | 4.8k views

+32 votes

8 answers

8

GATE1994-1.6, ISRO2008-29
The number of distinct simple graphs with up to three nodes is $15$ $10$ $7$ $9$

answered 4 days ago in Graph Theory by Saurabh666 (389 points) | 9.3k views

0 votes

1 answer

9

Rosen 7e Recurrence Relation Exercise-8.1 Question no-25 page no-511
How many bit sequences of length seven contain an even number of 0s? I'm trying to solve this using recurrence relation Is my approach correct? Let T(n) be the string having even number of 0s T(1)=1 {1} T(2)=2 {00, 11} T(3)=4 {001, ... add 0 to strings of length n-1 having odd number of 0s T(n)=T(n-1) Hence, we have T(n)=2T(n-1)

answered 6 days ago in Combinatory by anonymousgamer (11 points) | 53 views

+2 votes

3 answers

10

Made easy
What is the chromatic number of following graphs? 1) 2)

answered Oct 16 in Graph Theory by chirudeepnamini Active (1.8k points) | 167 views

0 votes

1 answer

11

Combinatorics
There are 6n flowers of one type and 3 flowers of second type, total no. Of garlands possible?

answered Oct 11 in Combinatory by shivamgo (11 points) | 29 views

+8 votes

4 answers

12

GATE1989-3-v
Answer the following: Which of the following well-formed formulas are equivalent? $P \rightarrow Q$ $\neg Q \rightarrow \neg P$ $\neg P \vee Q$ $\neg Q \rightarrow P$

answered Oct 8 in Mathematical Logic by vupadhayayx86 Active (1.4k points) | 587 views

+3 votes

2 answers

13

TIFR2010-Maths-A-1
A cyclic group of order 60 has 12 Generators 15 Generators 16 Generators 20 Generators

answered Oct 6 in Set Theory & Algebra by Lakshman Patel RJIT Veteran (51.5k points) | 940 views

+2 votes

3 answers

14

TIFR-2014-Maths-B-4
Let $H_{1}$, $H_{2}$ be two distinct subgroups of a finite group $G$, each of order $2$. Let $H$ be the smallest subgroup containing $H_{1}$ and $H_{2}$. Then the order of $H$ is Always 2 Always 4 Always 8 None of the above.

answered Oct 5 in Set Theory & Algebra by Harry Richie (17 points) | 328 views

+1 vote

1 answer

15

TIFR-2014-Maths-A-15
How many proper subgroups does the group $\mathbb{Z} &oplus; \mathbb{Z}$ have? $1$ $2$ $3$ Infinitely many

answered Oct 5 in Set Theory & Algebra by Harry Richie (17 points) | 182 views

+13 votes

2 answers

16

GATE2015-2-9
The number of divisors of $2100$ is ____.

answered Oct 3 in Set Theory & Algebra by JashanArora Junior (827 points) | 3.2k views

+5 votes

10 answers

17

GATE2019-21
The value of $3^{51} \text{ mod } 5$ is _____

answered Oct 3 in Combinatory by techbd123 Active (1.4k points) | 3k views

+1 vote

1 answer

18

graph Theory
Consider an undirected graph G where self-loops are not allowed. The vertex set of G is {(i,j):1<=i<=12,1<=j<=12}. There is an edge between (a, b) and (c, d) if |a-c|<=1 and |b-d|<=1. The number of edges in this graph is __________.

answered Oct 1 in Graph Theory by Mac2 (11 points) | 116 views

+5 votes

2 answers

19

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

answered Sep 27 in Set Theory & Algebra by techbd123 Active (1.4k points) | 237 views

+31 votes

3 answers

20

GATE2001-2.15
How many undirected graphs (not necessarily connected) can be constructed out of a given set $V=\{v_1, v_2, \dots v_n\}$ of $n$ vertices? $\frac{n(n-1)} {2}$ $2^n$ $n!$ $2^\frac{n(n-1)} {2} $

answered Sep 26 in Graph Theory by HeartBleed Junior (691 points) | 3.9k views

0 votes

1 answer

21

Kenneth Rosen Edition 7th Exercise 2.2 Question 14 (Page No. 136)
Find the sets $A$ and $B$ if $A-B=\left \{ 1,5,7,8 \right \}, B-A=\left \{ 2,10 \right \},$ and $A \cap B=\left \{ 3,6,9 \right \}.$

answered Sep 24 in Set Theory & Algebra by anurag_cs (41 points) | 15 views

0 votes

2 answers

22

Self-Doubt:Mathematical logic
“Every asymmetric relation is antisymmetric” Is this statement is True or False? I think it is false, because asymmetric relation never allows loops and antisymmetric relation allows loops. Am I not correct?

answered Sep 24 in Set Theory & Algebra by anurag_cs (41 points) | 31 views

+33 votes

9 answers

23

GATE2014-3-51
If $G$ is the forest with $n$ vertices and $k$ connected components, how many edges does $G$ have? $\left\lfloor\frac {n}{k}\right\rfloor$ $\left\lceil \frac{n}{k} \right\rceil$ $n-k$ $n-k+1$

answered Sep 24 in Graph Theory by HeartBleed Junior (691 points) | 4.4k views

+17 votes

6 answers

24

GATE1998-10a
Prove by induction that the expression for the number of diagonals in a polygon of $n$ sides is $\frac{n(n-3)}{2}$

answered Sep 20 in Set Theory & Algebra by Gaurav Yadav (233 points) | 1.2k views

+10 votes

3 answers

25

GATE1997-14
Let $R$ be a reflexive and transitive relation on a set $A$. Define a new relation $E$ on $A$ as $E=\{(a, b) \mid (a, b) \in R \text{ and } (b, a) \in R \}$ Prove that $E$ is an equivalence relation on $A$. Define a relation $\leq$ on the equivalence classes of $E$ ... $\exists a, b$ such that $a \in E_1, b \in E_2 \text{ and } (a, b) \in R$. Prove that $\leq$ is a partial order.

answered Sep 19 in Set Theory & Algebra by Sambhrant Maurya Active (3.2k points) | 806 views

+15 votes

4 answers

26

GATE1994-3.8
Give a relational algebra expression using only the minimum number of operators from $(∪, −)$ which is equivalent to $R$ $∩$ $S.$

answered Sep 18 in Set Theory & Algebra by Anurag007 (11 points) | 830 views

+3 votes

2 answers

27

UGCNET-June-2019-II-5
For which values of $m$ and $n$ does the complete bipartite graph $k_{m,n}$ have a Hamiltonian circuit ? $m\neq n,\ \ m,n \geq 2$ $m\neq n,\ \ m,n \geq 3$ $m=n,\ \ m,n \geq 2$ $m= n,\ \ m,n \geq 3$

answered Sep 17 in Graph Theory by Raghava45 (339 points) | 169 views

+23 votes

5 answers

28

GATE2009-23
Which one of the following is the most appropriate logical formula to represent the statement? "Gold and silver ornaments are precious". The following notations are used: $G(x): x$ is a gold ornament $S(x): x$ is a silver ornament $P(x): x$ ... $\exists x((G(x) \wedge S(x)) \implies P(x))$ $\forall x((G(x) \vee S(x)) \implies P(x))$

answered Sep 17 in Mathematical Logic by manikantsharma (375 points) | 1.7k views

+13 votes

3 answers

29

ISI Entrance Exam MTech (CS)
Consider all possible trees with $n$ nodes. Let $k$ be the number of nodes with degree greater than $1$ in a given tree. What is the maximum possible value of $k$?

answered Sep 14 in Graph Theory by rohith1001 Junior (549 points) | 936 views

0 votes

3 answers

30

Permutations and combinations
In how any ways can 8 different shirts be distributed among 4 different people so that each recieves 2 shirts?

answered Sep 13 in Combinatory by gajendercse (11 points) | 252 views

+20 votes

4 answers

31

GATE1996-8
Let $F$ be the collection of all functions $f: \{1, 2, 3\} \to \{1, 2, 3\}$. If $f$ and $g \in F$, define an equivalence relation $\sim$ by $f\sim g$ if and only if $f(3) = g(3)$. Find the number of equivalence classes defined by $\sim$. Find the number of elements in each equivalence class.

answered Sep 10 in Set Theory & Algebra by Debargha Bhattacharj Junior (653 points) | 1.6k views

+1 vote

1 answer

32

REGARDING DISCRETE MATHS SYLLABUS
FIELD AND RING ARE IN SYLLABUS???

answered Sep 10 in Set Theory & Algebra by Arjun Veteran (421k points) | 97 views

0 votes

2 answers

33

UGCNET-Dec2012-III-34
The power set of AUB, where A={2, 3, 5, 7} and B={2, 5, 8, 9}is 256 64 16 4

answered Sep 9 in Discrete Mathematics by omsanchitjain (33 points) | 900 views

+2 votes

2 answers

34

UGCNET-Dec2012-II-4
The power set of the set $\{ \Phi \}$ is $\{ \Phi \}$ $\{ \Phi, \{ \Phi \} \}$ $\{ 0 \}$ $\{ 0, \Phi , \{ \Phi \} \}$

answered Sep 9 in Set Theory & Algebra by omsanchitjain (33 points) | 485 views

+2 votes

3 answers

35

UGCNET-Dec2015-II-3
Which of the following is/are not true ? The set of negative integers is countable. The set of integers that are multiples of 7 is countable. The set of even integers is countable. The set of real numbers between 0 and 1⁄2 is countable. a and c b and d b only d only

answered Sep 9 in Set Theory & Algebra by omsanchitjain (33 points) | 726 views

0 votes

1 answer

36

Kenneth Rosen Edition 7th Exercise 1.6 Question 30 (Page No. 80)
Use resolution to show the hypotheses “Allen is a bad boy or Hillary is a good girl” and “Allen is a good boy or David is happy” imply the conclusion “Hillary is a good girl or David is happy.”

answered Sep 7 in Mathematical Logic by tejamach (11 points) | 13 views

+2 votes

1 answer

37

Countable and Uncountable Self Doubt 2
Which of the following is always correct? A. Cross product of two countable set is countable B. Cross product of two countable set is uncountable C. Cross product of two uncountable set is countable D. Cross product of uncountable ... E. Cross product of uncountable and countable set is countable F. Cross product of uncountable and countable set is uncountable

answered Sep 5 in Set Theory & Algebra by Sandee (11 points) | 95 views

+5 votes

3 answers

38

UGCNET-June-2019-II-1
Consider the poset $( \{3,5,9,15,24,45 \}, \mid).$ Which of the following is correct for the given poset ? There exist a greatest element and a least element There exist a greatest element but not a least element There exist a least element but not a greatest element There does not exist a greatest element and a least element

answered Sep 4 in Set Theory & Algebra by bhupendrakumar (45 points) | 460 views

+1 vote

1 answer

39

How do I prepare Engineering Mathematics for Gate CS?
Good Morning, I want to start Engineering Mathematics and need help from you to know where to start and what would be the best sequence to complete the whole subject?

answered Sep 4 in Mathematical Logic by Akashniranjan (11 points) | 479 views

+5 votes

2 answers

40

MadeEasy Test Series 2018: Graph Theory - Graph Coloring
answer given is 4. Please provide a detailed solution.

answered Sep 3 in Graph Theory by Rishav_Bhatt (141 points) | 158 views

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title	title:apple
content	content:apple
exclude	-tag:apple
force match	+apple
views	views:100
score	score:10
answers	answers:2
is accepted	isaccepted:true
is closed	isclosed:true

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