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Recent questions tagged discrete-mathematics
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votes
1
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181
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
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in
Others
Jan 29, 2021
by
soujanyareddy13
213
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cmi2018-datascience
discrete-mathematics
0
votes
2
answers
182
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
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in
Others
Jan 29, 2021
by
soujanyareddy13
334
views
cmi2018-datascience
matrix
linear-algebra
discrete-mathematics
0
votes
1
answer
183
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
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in
Others
Jan 29, 2021
by
soujanyareddy13
336
views
cmi2018-datascience
matrix
linear-algebra
discrete-mathematics
0
votes
1
answer
184
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
271
views
cmi2018-datascience
set-theory
discrete-mathematics
6
votes
1
answer
185
NIELIT Scientist B 2020 November: 84
Given the truth table of a Binary Operation \$ as follows: $ ... hline \end{array}$ Identify the matching Boolean Expression. $X \$ \neg Y$ $\neg X \$ Y$ $\neg X \$ \neg Y$ none of the options
gatecse
asked
in
Mathematical Logic
Dec 9, 2020
by
gatecse
667
views
nielit-scb-2020
mathematical-logic
propositional-logic
discrete-mathematics
3
votes
3
answers
186
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
3.5k
views
ugcnetcse-oct2020-paper2
discrete-mathematics
inclusion-exclusion
2
votes
2
answers
187
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
3.2k
views
ugcnetcse-oct2020-paper2
discrete-mathematics
combinatory
1
vote
3
answers
188
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
2.3k
views
ugcnetcse-oct2020-paper2
discrete-mathematics
mathematical-logic
1
vote
2
answers
189
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
913
views
ugcnetcse-oct2020-paper2
discrete-mathematics
graph-theory
0
votes
1
answer
190
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
1.1k
views
ugcnetcse-oct2020-paper2
discrete-mathematics
mathematical-logic
1
vote
1
answer
191
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
1.0k
views
ugcnetcse-oct2020-paper2
discrete-mathematics
mathematical-logic
2
votes
2
answers
192
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 $i$ Only $iii$ Both $i$ and $ii$ $ii$ and not $i$
go_editor
asked
in
Mathematical Logic
Nov 20, 2020
by
go_editor
1.1k
views
ugcnetcse-oct2020-paper2
discrete-mathematics
set-theory&algebra
relations
2
votes
1
answer
193
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
971
views
ugcnetcse-oct2020-paper2
discrete-mathematics
first-order-logic
0
votes
1
answer
194
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 ... incorrect $(ii)$ and $(iii)$ are incorrect $(ii)$ and $(v)$ are incorrect $(i)$ and $(iv)$ are incorrect
go_editor
asked
in
Mathematical Logic
Nov 20, 2020
by
go_editor
1.6k
views
ugcnetcse-oct2020-paper2
discrete-mathematics
graph-theory
2
votes
1
answer
195
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. $(R \wedge E) \Leftrightarrow C$ ... given below: $(ii)$ only $(iii)$ only $(i)$ and $(iii)$ only $(ii)$ and $(iv)$ only
go_editor
asked
in
Mathematical Logic
Nov 20, 2020
by
go_editor
2.1k
views
ugcnetcse-oct2020-paper2
discrete-mathematics
propositional-logic
0
votes
0
answers
196
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
620
views
ugcnetcse-oct2020-paper2
discrete-mathematics
graph-theory
0
votes
1
answer
197
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 $14.$
admin
asked
in
Combinatory
May 9, 2020
by
admin
1.2k
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
0
votes
1
answer
198
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?
admin
asked
in
Combinatory
May 9, 2020
by
admin
528
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
0
votes
2
answers
199
Kenneth Rosen Edition 7 Exercise 8.3 Question 14 (Page No. 535)
Suppose that there are $n = 2^{k}$ teams in an elimination tournament, where there are $\frac{n}{2}$ games in the first round, with the $\frac{n}{2} = 2^{k-1}$ winners playing in the second round, and so on. Develop a recurrence relation for the number of rounds in the tournament.
admin
asked
in
Combinatory
May 9, 2020
by
admin
1.8k
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
0
votes
1
answer
200
Kenneth Rosen Edition 7 Exercise 8.3 Question 13 (Page No. 535)
Give a big-O estimate for the function $f$ given below if $f$ is an increasing function. $f (n) = 2f (n/3) + 4 \:\text{with}\: f (1) = 1.$
admin
asked
in
Combinatory
May 9, 2020
by
admin
557
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
1
vote
2
answers
201
Kenneth Rosen Edition 7 Exercise 8.3 Question 12 (Page No. 535)
Find $f (n)$ when $n = 3k,$ where $f$ satisfies the recurrence relation $f (n) = 2f (n/3) + 4 \:\text{with}\: f (1) = 1.$
admin
asked
in
Combinatory
May 9, 2020
by
admin
631
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
0
votes
1
answer
202
Kenneth Rosen Edition 7 Exercise 8.3 Question 11 (Page No. 535)
Give a big-O estimate for the function $f$ in question $10$ if $f$ is an increasing function.
admin
asked
in
Combinatory
May 9, 2020
by
admin
356
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
0
votes
1
answer
203
Kenneth Rosen Edition 7 Exercise 8.3 Question 10 (Page No. 535)
Find $f (n)$ when $n = 2^{k},$ where $f$ satisfies the recurrence relation $f (n) = f (n/2) + 1 \:\text{with}\: f (1) = 1.$
admin
asked
in
Combinatory
May 9, 2020
by
admin
366
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
0
votes
1
answer
204
Kenneth Rosen Edition 7 Exercise 8.3 Question 9 (Page No. 535)
Suppose that $f (n) = f (n/5) + 3n^{2}$ when $n$ is a positive integer divisible by $5, \:\text{and}\: f (1) = 4.$ Find $f (5)$ $f (125)$ $f (3125)$
admin
asked
in
Combinatory
May 9, 2020
by
admin
395
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
0
votes
1
answer
205
Kenneth Rosen Edition 7 Exercise 8.3 Question 8 (Page No. 535)
Suppose that $f (n) = 2f (n/2) + 3$ when $n$ is an even positive integer, and $f (1) = 5.$ Find $f (2)$ $f (8)$ $f (64)$ $(1024)$
admin
asked
in
Combinatory
May 9, 2020
by
admin
703
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
0
votes
1
answer
206
Kenneth Rosen Edition 7 Exercise 8.3 Question 7 (Page No. 535)
Suppose that $f (n) = f (n/3) + 1$ when $n$ is a positive integer divisible by $3,$ and $f (1) = 1.$ Find $f (3)$ $f (27)$ $f (729)$
admin
asked
in
Combinatory
May 9, 2020
by
admin
478
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
0
votes
0
answers
207
Kenneth Rosen Edition 7 Exercise 8.3 Question 6 (Page No. 535)
How many operations are needed to multiply two $32 \times 32$ matrices using the algorithm referred to in Example $5?$
admin
asked
in
Combinatory
May 9, 2020
by
admin
350
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
0
votes
0
answers
208
Kenneth Rosen Edition 7 Exercise 8.3 Question 5 (Page No. 535)
Determine a value for the constant C in Example $4$ and use it to estimate the number of bit operations needed to multiply two $64$-bit integers using the fast multiplication algorithm.
admin
asked
in
Combinatory
May 9, 2020
by
admin
247
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
0
votes
1
answer
209
Kenneth Rosen Edition 7 Exercise 8.3 Question 4 (Page No. 535)
Express the fast multiplication algorithm in pseudocode.
admin
asked
in
Combinatory
May 9, 2020
by
admin
361
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
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