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Recent questions tagged discrete-mathematics
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61
Nptel Assignment Question
Let P(n) be a statement and we prove P(k) ⇒ $P(k^{2})$ and P(k) ⇒ P(k + 3). Then we to prove that P(n) is true for all n (a) it is enough to prove the base case for k = 1 (b) it is enough to prove the base case for k = 1 and k = 2. (c) it is enough to prove that base case for k = 1 and k = 2 and k = 3 (d) No base case can prove the statement.
rsansiya111
asked
in
Set Theory & Algebra
Dec 3, 2021
by
rsansiya111
211
views
nptel-quiz
discrete-mathematics
0
votes
0
answers
62
Nptel Assignment Question
Let P(n) be a statement and we prove P(k) ⇒ P(k − 3) and P(k) ⇒ P(2k). Then we to prove that P(n) is true for all n (a) it is enough to prove the base case for k = 1 (b) it is enough to prove the base case for k = 1 and k = 2. (c) it is enough to prove that base case for k = 1 and k = 2 and k = 3 (d) No base case can prove the statement
rsansiya111
asked
in
Set Theory & Algebra
Dec 3, 2021
by
rsansiya111
105
views
nptel-quiz
discrete-mathematics
2
votes
1
answer
63
Applied Grand Test 2
Consider the equivalence relation R induced by the partition P={{1},{3},{2,4,5,6}} of set A={1,2,3,4,5,6}. The number of ordered pairs in R is ____
LRU
asked
in
Set Theory & Algebra
Nov 22, 2021
by
LRU
229
views
test-series
discrete-mathematics
set-theory&algebra
3
votes
3
answers
64
Applied Test Series
The number of possible ways in which 5 identical helicopters can take off given that we are having 5 helipads.____
LRU
asked
in
Combinatory
Nov 9, 2021
by
LRU
326
views
test-series
engineering-mathematics
discrete-mathematics
combinatory
1
vote
1
answer
65
Applied Test Series
There are 4 parts of an encyclopedia which are available in a library which are arranged on the shelf along with other books on a shelf which add up to a total 25 books, if the books are arranged randomly then the number of ways in which the encyclopedia is in the correct order is (the parts need not be beside each other)____
LRU
asked
in
Combinatory
Nov 9, 2021
by
LRU
173
views
test-series
engineering-mathematics
discrete-mathematics
combinatory
1
vote
1
answer
66
Combinatorics Question| Discrete Maths
Suppose there are 4 cricket matches to be played in 3 grounds. The number of ways the matches can be assigned to the grounds so that each ground gets at least one match is
Acejoy
asked
in
Combinatory
Oct 25, 2021
by
Acejoy
225
views
discrete-mathematics
combinatory
2
votes
1
answer
67
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?_________
LRU
asked
in
Combinatory
Oct 15, 2021
by
LRU
272
views
test-series
discrete-mathematics
combinatory
0
votes
1
answer
68
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?
LRU
asked
in
Mathematical Logic
Sep 26, 2021
by
LRU
330
views
pigeonhole-principle
discrete-mathematics
test-series
2
votes
2
answers
69
CMI-2018-DataScience-A: 3
Let $x=\begin{bmatrix} 3& 1 & 2 \end{bmatrix}$. Which of the following statements are true? $x^Tx$ is a $3\times 3$ matrix $xx^T$ is a $3\times 3$ matrix $xx^T$ is a $1\times 1$ matrix $xx^T=x^Tx$
soujanyareddy13
asked
in
Others
Jan 29, 2021
by
soujanyareddy13
264
views
cmi2018-datascience
matrix
linear-algebra
discrete-mathematics
1
vote
1
answer
70
CMI-2018-DataScience-A: 4
A $n\times n$ matrix $A$ is said to be $symmetric$ if $A^T=A$. Suppose $A$ is an arbitrary $2\times 2$ matrix. Then which of the following matrices are symmetric (here $0$ denotes the $2\times 2$ matrix consisting of zeros): $A^TA$ $\begin{bmatrix} 0&A^T \\ A & 0 \end{bmatrix}$ $AA^T$ $\begin{bmatrix} A & 0 \\ 0 & A^T \end{bmatrix}$
soujanyareddy13
asked
in
Others
Jan 29, 2021
by
soujanyareddy13
316
views
cmi2018-datascience
matrix
linear-algebra
discrete-mathematics
0
votes
1
answer
71
CMI-2018-DataScience-A: 14
Consider the following functions defined from the interval $(0,1)$ to real numbers. Which of these functions attain their maximum value in the interval $(0,1)?$ $f(x)=\frac{1}{x(1-x)}$ $g(x)=-(x-0.75)^2$ $u(x)=\sin(\frac{\pi x}{2})$ $v(x)=x^2+2x$
soujanyareddy13
asked
in
Others
Jan 29, 2021
by
soujanyareddy13
294
views
cmi2018-datascience
functions
discrete-mathematics
0
votes
1
answer
72
CMI-2018-DataScience-B: 1
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc. Let $N=\{1,2,3,...\}$ be the set of natural integers and let $f:N\times N \mapsto N$ be defined by $f(m,n)=(2m-1)*2^n.$Is $f$ injective? Is $f$ surjective? Give reasons.
soujanyareddy13
asked
in
Others
Jan 29, 2021
by
soujanyareddy13
120
views
cmi2018-datascience
discrete-mathematics
0
votes
2
answers
73
CMI-2018-DataScience-B: 2
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc. Suppose $A,B$ and $C$ are $m\times m$ matrices. What does the following algorithm compute? (Here $A(i,j)$ ... .) for i=1 to m for j=1 to m for k=1 to m C(i,j)=A(i,k)*B(k,j)+C(i,j) end end end
soujanyareddy13
asked
in
Others
Jan 29, 2021
by
soujanyareddy13
204
views
cmi2018-datascience
matrix
linear-algebra
discrete-mathematics
0
votes
1
answer
74
CMI-2018-DataScience-B: 4
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc. In computing, a floating point operation (flop) is any one of the following operations ... . How does this number change if both the matrices are upper triangular?
soujanyareddy13
asked
in
Others
Jan 29, 2021
by
soujanyareddy13
201
views
cmi2018-datascience
matrix
linear-algebra
discrete-mathematics
0
votes
1
answer
75
CMI-2018-DataScience-B: 5
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc. A function $f$ from the set $A$ to itself is said to have a fixed point if $f(i)=i$ ... $A$ is the set $\{a,b,c,d\}$. Find the number of bijective functions from the set $A$ to itself having no fixed point.
soujanyareddy13
asked
in
Others
Jan 29, 2021
by
soujanyareddy13
168
views
cmi2018-datascience
set-theory
discrete-mathematics
2
votes
1
answer
76
NIELIT Scientist B 2020 November: 84
Given the truth table of a Binary Operation \$ as follows: $ ... 1 }\\ \hline \end{array}$ Identify the matching Boolean Expression. $X \$ ┐ Y$ $┐ X \$ Y$ $┐ X \$ ┐ Y$ none of the options
gatecse
asked
in
Mathematical Logic
Dec 9, 2020
by
gatecse
166
views
nielit-scb-2020
mathematical-logic
propositional-logic
discrete-mathematics
3
votes
3
answers
77
UGC NET CSE | October 2020 | Part 2 | Question: 1
The number of positive integers not exceeding $100$ that are either odd or the square of an integer is _______ $63$ $59$ $55$ $50$
go_editor
asked
in
Set Theory & Algebra
Nov 20, 2020
by
go_editor
2.2k
views
ugcnetcse-oct2020-paper2
discrete-mathematics
inclusion-exclusion
2
votes
2
answers
78
UGC NET CSE | October 2020 | Part 2 | Question: 2
How many ways are there to pack six copies of the same book into four identical boxes, where a box can contain as many as six books? $4$ $6$ $7$ $9$
go_editor
asked
in
Combinatory
Nov 20, 2020
by
go_editor
2.2k
views
ugcnetcse-oct2020-paper2
discrete-mathematics
combinatory
1
vote
2
answers
79
UGC NET CSE | October 2020 | Part 2 | Question: 3
Which of the following pairs of propositions are not logically equivalent? $((p \rightarrow r) \wedge (q \rightarrow r))$ and $((p \vee q) \rightarrow r)$ $p \leftrightarrow q$ and $(\neg p \leftrightarrow \neg q)$ ... and $p \leftrightarrow q$ $((p \wedge q) \rightarrow r)$ and $((p \rightarrow r) \wedge (q \rightarrow r))$
go_editor
asked
in
Discrete Mathematics
Nov 20, 2020
by
go_editor
1.7k
views
ugcnetcse-oct2020-paper2
discrete-mathematics
mathematical-logic
1
vote
1
answer
80
UGC NET CSE | October 2020 | Part 2 | Question: 26
Let $G$ be a directed graph whose vertex set is the set of numbers from $1$ to $100$. There is an edge from a vertex $i$ to a vertex $j$ if and only if either $j=i+1$ or $j=3i$. The minimum number of edges in a path in $G$ from vertex $1$ to vertex $100$ is ______ $23$ $99$ $4$ $7$
go_editor
asked
in
Discrete Mathematics
Nov 20, 2020
by
go_editor
643
views
ugcnetcse-oct2020-paper2
discrete-mathematics
graph-theory
0
votes
1
answer
81
UGC NET CSE | October 2020 | Part 2 | Question: 37
If $f(x)=x$ is my friend, and $p(x) =x$ is perfect, then correct logical translation of the statement “some of my friends are not perfect” is ______ $\forall _x (f(x) \wedge \neg p(x))$ $\exists _x (f(x) \wedge \neg p(x))$ $\neg (f(x) \wedge \neg p(x))$ $\exists _x (\neg f(x) \wedge \neg p(x))$
go_editor
asked
in
Discrete Mathematics
Nov 20, 2020
by
go_editor
701
views
ugcnetcse-oct2020-paper2
discrete-mathematics
mathematical-logic
1
vote
1
answer
82
UGC NET CSE | October 2020 | Part 2 | Question: 38
What kind of clauses are available in conjunctive normal form? Disjunction of literals Disjunction of variables Conjunction of literals Conjunction of variables
go_editor
asked
in
Discrete Mathematics
Nov 20, 2020
by
go_editor
782
views
ugcnetcse-oct2020-paper2
discrete-mathematics
mathematical-logic
2
votes
2
answers
83
UGC NET CSE | October 2020 | Part 2 | Question: 39
Consider the following properties: Reflexive Antisymmetric Symmetric Let $A=\{a,b,c,d,e,f,g\}$ and $R=\{(a,a), (b,b), (c,d), (c,g), (d,g), (e,e), (f,f), (g,g)\}$ be a relation on $A$. Which of the following property (properties) is (are) satisfied by the relation $R$? Only $a$ Only $c$ Both $a$ and $b$ $b$ and not $a$
go_editor
asked
in
Discrete Mathematics
Nov 20, 2020
by
go_editor
774
views
ugcnetcse-oct2020-paper2
discrete-mathematics
set-theory&algebra
relations
1
vote
1
answer
84
UGC NET CSE | October 2020 | Part 2 | Question: 40
Consider the following argument with premise $\forall _x (P(x) \vee Q(x))$ and conclusion $(\forall _x P(x)) \wedge (\forall _x Q(x))$ ... $(E)$ are not correct inferences Steps $(D)$ and $(F)$ are not correct inferences Step $(G)$ is not a correct inference
go_editor
asked
in
Discrete Mathematics
Nov 20, 2020
by
go_editor
617
views
ugcnetcse-oct2020-paper2
discrete-mathematics
first-order-logic
0
votes
1
answer
85
UGC NET CSE | October 2020 | Part 2 | Question: 53
Consider the following statements: Any tree is $2$-colorable A graph $G$ has no cycles of even length if it is bipartite A graph $G$ is $2$-colorable if is bipartite A graph $G$ can be colored with $d+1$ colors if $d$ is the maximum degree of ... incorrect $(b)$ and $(c)$ are incorrect $(b)$ and $(e)$ are incorrect $(a)$ and $(d)$ are incorrect
go_editor
asked
in
Discrete Mathematics
Nov 20, 2020
by
go_editor
1.1k
views
ugcnetcse-oct2020-paper2
discrete-mathematics
graph-theory
1
vote
1
answer
86
UGC NET CSE | October 2020 | Part 2 | Question: 61
Consider the statement below. A person who is radical $(R)$ is electable $(E)$ if he/she is conservative $(C)$, but otherwise not electable. Few probable logical assertions of the above sentence are given below. $(R \wedge E) \Leftrightarrow C$ ... options given below: $(B)$ only $(C)$ only $(A)$ and $(C)$ only $(B)$ and $(D)$ only
go_editor
asked
in
Discrete Mathematics
Nov 20, 2020
by
go_editor
1.2k
views
ugcnetcse-oct2020-paper2
discrete-mathematics
propositional-logic
0
votes
0
answers
87
UGC NET CSE | October 2020 | Part 2 | Question: 86
Let $G$ be a simple undirected graph, $T_D$ be a DFS tree on $G$, and $T_B$ be the BFS tree on $G$. Consider the following statements. Statement $I$: No edge of $G$ is a cross with respect to $T_D$ Statement $II$: ... Statement $II$ are false Statement $I$ is correct but Statement $II$ is false Statement $I$ is incorrect but Statement $II$ is true
go_editor
asked
in
Discrete Mathematics
Nov 20, 2020
by
go_editor
429
views
ugcnetcse-oct2020-paper2
discrete-mathematics
graph-theory
0
votes
1
answer
88
Kenneth Rosen Edition 7 Exercise 8.3 Question 16 (Page No. 535)
Solve the recurrence relation for the number of rounds in the tournament described in question $14.$
Lakshman Patel RJIT
asked
in
Combinatory
May 10, 2020
by
Lakshman Patel RJIT
829
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
0
votes
1
answer
89
Kenneth Rosen Edition 7 Exercise 8.3 Question 15 (Page No. 535)
How many rounds are in the elimination tournament described in question $14$ when there are $32$ teams?
Lakshman Patel RJIT
asked
in
Combinatory
May 10, 2020
by
Lakshman Patel RJIT
339
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
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