Recent questions and answers in Discrete Mathematics

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1 answer

1

Applied Test Series
A Professor tells 3 Jokes in his maths class each year. How large a set of jokes does the professor need in order never to repeat the exact same triple of jokes over a period of 12 years?_________

Sudhanshu10 answered in Combinatory 5 days ago

28 views

16 votes

4 answers

2

GATE CSE 2002 | Question: 1.6
Which of the following is true? The set of all rational negative numbers forms a group under multiplication. The set of all non-singular matrices forms a group under multiplication. The set of all matrices forms a group under multiplication. Both B and C are true.

imkeshav answered in Set Theory & Algebra Oct 15

6.4k views

32 votes

5 answers

3

GATE CSE 2003 | Question: 5
$n$ couples are invited to a party with the condition that every husband should be accompanied by his wife. However, a wife need not be accompanied by her husband. The number of different gatherings possible at the party is \(^{2n}\mathrm{C}_n\times 2^n\) \(3^n\) \(\frac{(2n)!}{2^n}\) \(^{2n}\mathrm{C}_n\)

Arpit Patel answered in Combinatory Oct 13

5.7k views

2 votes

3 answers

4

NIELIT 2017 July Scientist B (IT) - Section B: 13
Which of the following statements is false? $(P\land Q)\lor(\sim P\land Q)\lor(P \land \sim Q)$ is equal to $\sim Q\land \sim P$ $(P\land Q)\lor(\sim P\land Q)\lor(P \wedge \sim Q)$ is equal to $Q\lor P$ ... $(P\land Q)\lor(\sim P\land Q)\lor (P \land \sim Q)$ is equal to $P\lor (Q\land \sim P)$

Mohitdas answered in Mathematical Logic Oct 11

314 views

51 votes

14 answers

5

GATE CSE 2015 Set 3 | Question: 5
The number of $4$ digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set $\{1, 2, 3\}$ is ________.

Kanwae Kan answered in Combinatory Oct 11

8.8k views

10 votes

6 answers

6

GATE CSE 2021 Set 1 | Question: 36
Let $G=(V, E)$ be an undirected unweighted connected graph. The diameter of $G$ is defined as: $\text{diam}(G)=\displaystyle \max_{u,v\in V} \{\text{the length of shortest path between $u$ and $v$}\}$ Let $M$ be the adjacency matrix of $G$. Define graph $G_2$ ... $\text{diam}(G_2) = \text{diam}(G)$ $\text{diam}(G)< \text{diam}(G_2)\leq 2\; \text{diam}(G)$

Nihal Singh answered in Graph Theory Oct 8

1.8k views

7 votes

4 answers

7

GATE CSE 2021 Set 2 | Question: 15
Choose the correct choice(s) regarding the following proportional logic assertion $S$: $S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \rightarrow R))$ $S$ is neither a tautology nor a contradiction $S$ is a tautology $S$ is a contradiction The antecedent of $S$ is logically equivalent to the consequent of $S$

Mohitdas answered in Mathematical Logic Oct 8

1.5k views

2 votes

5 answers

8

GATE CSE 2021 Set 1 | Question: 16
In an undirected connected planar graph $G$, there are eight vertices and five faces. The number of edges in $G$ is _________.

kalam_11 answered in Graph Theory Oct 6

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0 votes

1 answer

9

Kenneth Rosen Edition 7th Exercise 2.3 Question 35 (Page No. 154)
If $f$ and $fog$ are onto, does it follow that $g$ is onto?Justify your answer.

Vishal_kumar98 answered in Set Theory & Algebra Sep 30

by Vishal_kumar98

92 views

0 votes

1 answer

10

GATE ACADEMY TEST SERIES
What is the minimum number of students, each of whom comes from one of the 50 states, who must be enrolled in a university to guarantee that there are at least 100 who come from the same state?

raja11sep answered in Mathematical Logic Sep 26

89 views

0 votes

0 answers

11

Biconditional Operator in the logical expression for Symmetric Relation.
"The logical expression for the symmetric relation should contain the biconditional operator <-> instead of implication -> . Because, if u keep ->, then for the case when F -> T the ... " Could someone plz help, this seems to be correct. Also https://en.wikipedia.org/wiki/Symmetric_relation.

SHM asked in Mathematical Logic Sep 26

by SHM

28 views

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1 answer

12

Kenneth Rosen Edition 6th Exercise 2.2 Question 8 (Page No. 120)
Determine whether these statements are true or false. ∅ ∈ {∅} ∅ ∈ {∅, {∅}} {∅} ∈ {∅} {∅} ∈ {{∅}} {∅} ⊂ {∅, {∅}} {{∅}} ⊂ {∅, {∅}} {{∅}} ⊂ {{∅}, {∅}}

its_vaibhav answered in Set Theory & Algebra Sep 23

86 views

7 votes

3 answers

13

GATE CSE 1988 | Question: 13iii
Are the two digraphs shown in the above figure isomorphic? Justify your answer.

Pkaryan123 answered in Graph Theory Sep 21

638 views

23 votes

7 answers

14

GATE CSE 2015 Set 1 | Question: 54
Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is_______________.

Prarbdh Tiwari answered in Graph Theory Sep 20

by Prarbdh Tiwari

13.6k views

0 votes

1 answer

15

Rajat Agrawal007 answered in Set Theory & Algebra Sep 16

by Rajat Agrawal007

141 views

1 vote

1 answer

16

gateacademy test series
There are 12 stations on a rail route. How many ways a special train can stop at 4 of these stations, so that no two stops are consecutive stations? please explain in detail

Nibchee answered in Combinatory Sep 16

61 views

0 votes

1 answer

17

Marks Distribution for Engineering and Discrete Maths
Hey all, As per brochure there will be 13 marks alloted for engineering maths. My quer is whether discrete maths will too be included in this 13 marks i.e. EM+DM=13, or Discrete maths will have separate marks? Like in Gate 2021 paper , the combined marks for Engineering and Discrete maths was over 13.

Arjun answered in Mathematical Logic Sep 12

by Arjun

66 views

0 votes

1 answer

18

gateacademy testseries
In how many ways can seven different jobs be assigned to four different employees so that each employee is assigned at least one job and the most difficult job is assigned to the best employee?

nishant.singhal.cs answered in Combinatory Sep 8

by nishant.singhal.cs

55 views

0 votes

1 answer

19

Kenneth H Rosen 7th edition
Please see example 6. l am not getting the mathematical insight. Can anyone please tell how they are arriving at the answer.

Sahiltam answered in Combinatory Sep 7

292 views

3 votes

3 answers

20

KENETH ROSEN
How many different ways are there to seat four people around a circular table, where two seatings are considered the same when each person has the same left neighbor and the same right neighbor? ANSWER IS 6 OR 3 .????

M_eight answered in Combinatory Sep 7

1.3k views

0 votes

1 answer

21

Kenneth Rosen Edition 7th Exercise 6.4 Question 16 (Page No. 421)
Use question $14$ and Corollary $1$ to show that if $n$ is an integer greater than $1,$ then $\binom{n}{\left \lfloor n/2 \right \rfloor}\geq \frac{2^{n}}{2}.$ Conclude from part $(A)$ that if $n$ is a positive integer, then $\binom{2n}{n}\geq \frac{4^{n}}{2n}.$

harsh_sojitra answered in Combinatory Sep 6

by harsh_sojitra

51 views

0 votes

3 answers

22

Kenneth Rosen Edition 7th Exercise 6.1 Question 2 (Page No. 396)
An office building contains $27$ floors and has $37$ offices on each floor. How many offices are in the building?

harsh_sojitra answered in Combinatory Sep 6

by harsh_sojitra

78 views

19 votes

4 answers

23

CMI2014-A-01
For the inter-hostel six-a-side football tournament, a team of $6$ players is to be chosen from $11$ players consisting of $5$ forwards, $4$ defenders and $2$ goalkeepers. The team must include at least $2$ forwards, at least $2$ defenders and at least $1$ goalkeeper. Find the number of different ways in which the team can be chosen. $260$ $340$ $720$ $440$

Nirmalya Pratap 1 answered in Combinatory Sep 5

by Nirmalya Pratap 1

1.4k views

18 votes

5 answers

24

GATE CSE 1989 | Question: 1-iv
The transitive closure of the relation $\left\{(1, 2), (2, 3), (3, 4), (5, 4)\right\}$ on the set $\left\{1, 2, 3, 4, 5\right\}$ is ___________.

raja11sep answered in Set Theory & Algebra Sep 4

4.1k views

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1 answer

25

NIELIT 2017 July Scientist B (IT) - Section B: 15
The number of diagonals that can be drawn by joining the vertices of an octagon is $28$ $48$ $20$ None of the option

M_eight answered in Graph Theory Aug 28

227 views

29 votes

4 answers

26

GATE CSE 1996 | Question: 2.2
Let $R$ be a non-empty relation on a collection of sets defined by $_{A}R_ B$ if and only if $A \cap B = \phi$. Then, (pick the true statement) $A$ is reflexive and transitive $R$ is symmetric and not transitive $R$ is an equivalence relation $R$ is not reflexive and not symmetric

Varn Gupta answered in Set Theory & Algebra Aug 28

10.1k views

22 votes

6 answers

27

GATE IT 2004 | Question: 5
What is the maximum number of edges in an acyclic undirected graph with $n$ vertices? $n-1$ $n$ $n+1$ $2n-1$

raja11sep answered in Graph Theory Aug 28

4.3k views

2 votes

3 answers

28

UGCNET-Dec2015-II: 6
Which of the following arguments are not valid ? "If Gora gets the job and works hard, then he will be promoted. if Gora gets promotion, then he will be happy. He will not be happy, therefore, either he will not get the job or he will not work hard." "Either Puneet is not ... $n^2 > 1$, then $n>1$. a and c b and c a,b, and c a and b

forever_Learner answered in Mathematical Logic Aug 25

by forever_Learner

3.1k views

0 votes

1 answer

29

Kenneth Rosen Edition 7th Exercise 6.4 Question 18 (Page No. 421)
Suppose that $b$ is an integer with $b \geq 7.$ Use the binomial theorem and the appropriate row of Pascal’s triangle to find the base-$b$ expansion of $(11)^{4}_{b}$ [that is, the fourth power of the number $(11)_{b}$ in base-$b$ notation].

harsh_sojitra answered in Combinatory Aug 23

by harsh_sojitra

83 views

52 votes

5 answers

30

GATE CSE 2016 Set 1 | Question: 1
Let $p, q, r, s$ represents the following propositions. $p:x\in\left\{8, 9, 10, 11, 12\right\}$ $q:$ $x$ is a composite number. $r:$ $x$ is a perfect square. $s:$ $x$ is a prime number. The integer $x\geq2$ which satisfies $\neg\left(\left(p\Rightarrow q\right) \wedge \left(\neg r \vee \neg s\right)\right)$ is ____________.

subbus answered in Mathematical Logic Aug 21

by subbus

7.8k views

2 votes

2 answers

31

Kenneth Rosen Edition 6th Exercise 1.1 Question 23 (Page No. 18)
State the converse, contrapositive, and inverse of each of these conditional statements. If it snows today, I will ski tomorrow. I come to class whenever there is going to be a quiz. A positive integer is a prime only if it has no divisors other than 1 and itself.

sabin324 answered in Mathematical Logic Aug 19

502 views

20 votes

6 answers

32

GATE CSE 2008 | Question: 31
$P$ and $Q$ are two propositions. Which of the following logical expressions are equivalent? $P ∨ \neg Q$ $\neg(\neg P ∧ Q)$ $(P ∧ Q) ∨ (P ∧ \neg Q) ∨ (\neg P ∧ \neg Q)$ $(P ∧ Q) ∨ (P ∧ \neg Q) ∨ (\neg P ∧ Q)$ Only I and II Only I, II and III Only I, II and IV All of I, II, III and IV

Renga98 answered in Mathematical Logic Aug 17

4.8k views

38 votes

3 answers

33

GATE CSE 2005 | Question: 41
What is the first order predicate calculus statement equivalent to the following? "Every teacher is liked by some student" $∀(x)\left[\text{teacher}\left(x\right) → ∃(y) \left[\text{student}\left(y\right) → \text{likes}\left(y,x\right)\right]\right]$ ...

Renga98 answered in Mathematical Logic Aug 16

7.4k views

9 votes

2 answers

34

functions-combinations
Assume an almost injective function is a function in which exactly two element from domain maps to a single element in co-domain, otherwise function is injective. $S$ and $R$ are sets with cardinality $m$ and $n$ respectively. $(m<n)$ and $m\geq 2$. Number of almost injective ... $\frac{( n-m)!}{ 2}$ put m=2 and n=5. we get almost injective functions=5 shudnt it be C?

rish1602 answered in Mathematical Logic Aug 15

509 views

12 votes

4 answers

35

GATE CSE 2020 | Question: 52
Graph $G$ is obtained by adding vertex $s$ to $K_{3,4}$ and making $s$ adjacent to every vertex of $K_{3,4}$. The minimum number of colours required to edge-colour $G$ is _______

sridhar15399 answered in Graph Theory Aug 7

by sridhar15399

5.6k views

17 votes

5 answers

36

CMI2013-A-07
Consider the following two statements. There are infinitely many interesting whole numbers. There are finitely many uninteresting whole numbers. Which of the following is true? Statements $1$ and $2$ are equivalent. Statement $1$ implies statement $2$. Statement $2$ implies statement $1$. None of the above.

rish1602 answered in Mathematical Logic Aug 7

1.2k views

45 votes

6 answers

37

GATE CSE 2013 | Question: 26
The line graph $L(G)$ of a simple graph $G$ is defined as follows: There is exactly one vertex $v(e)$ in $L(G)$ for each edge $e$ in $G$. For any two edges $e$ and $e'$ in $G$, $L(G)$ has an edge between $v(e)$ and $v(e')$, if and only if $e$ ... of a planar graph is planar. (S) The line graph of a tree is a tree. $P$ only $P$ and $R$ only $R$ only $P, Q$ and $S$ only

sridhar15399 answered in Graph Theory Aug 6

by sridhar15399

12.1k views

23 votes

3 answers

38

TIFR2012-A-3
Long ago,in a planet far far away, there lived three races of intelligent inhabitants: the blues (who always tell the truth), the whites (who always lie), and the pinks (who, when asked a series of questions, start with a lie and then tell the truth and lie alternately). To ... $C$ is Pink. $A$ is White, $B$ is Pink, $C$ is Blue. Cannot be determined from the above data.

rish1602 answered in Mathematical Logic Aug 4

1.5k views

30 votes

7 answers

39

GATE IT 2004 | Question: 31
Let $p, q, r$ and $s$ be four primitive statements. Consider the following arguments: $P: [(¬p\vee q) ∧ (r → s) ∧ (p \vee r)] → (¬s → q)$ $Q: [(¬p ∧q) ∧ [q → (p → r)]] → ¬r$ $R: [[(q ∧ r) → p] ∧ (¬q \vee p)] → r$ $S: [p ∧ (p → r) ∧ (q \vee ¬ r)] → q$ Which of the above arguments are valid? $P$ and $Q$ only $P$ and $R$ only $P$ and $S$ only $P, Q, R$ and $S$

Dharmesh Dubey answered in Mathematical Logic Aug 2

by Dharmesh Dubey

6.1k views

37 votes

6 answers

40

GATE CSE 2017 Set 1 | Question: 29
Let $p$, $q$ and $r$ be propositions and the expression $\left ( p\rightarrow q \right )\rightarrow r$ be a contradiction. Then, the expression $\left ( r\rightarrow p \right )\rightarrow q$ is a tautology a contradiction always TRUE when $p$ is FALSE always TRUE when $q$ is TRUE

Dharmesh Dubey answered in Mathematical Logic Aug 2

by Dharmesh Dubey

6.3k views

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