Hot questions in Discrete Mathematics / GATE Overflow for GATE CSE

11 votes

1 answer

2221

TIFR CSE 2018 | Part B | Question: 10
For two $n$ bit strings $x,y \in\{0,1\}^{n},$ define $z=x\oplus y$ to be the bitwise XOR of the two strings (that is, if $x_{i},y_{i},z_{i}$ denote the $i^{th}$ bits of $x,y,z$ respectively, then $z_{i}=x_{i}+y_{i} \bmod 2$ ... such linear functions for $n \geq 2$ is: $2^{n}$ $2^{n^{2}}$ $\large2^{\frac{n}{2}}$ $2^{4n}$ $2^{n^{2}+n}$

For two $n$ bit strings $x,y \in\{0,1\}^{n},$ define $z=x\oplus y$ to be the bitwise XOR of the two strings (that is, if $x_{i},y_{i},z_{i}$ denote the $i^{th}$ bits of $...

Arjun

1.6k views

Arjun asked Dec 10, 2017

1 votes

2 answers

2222

UGC NET CSE | July 2018 | Part 2 | Question: 90
Which of the following statements is true? $(Z, \leq)$ is not totally ordered The set inclusion relation $\subseteq$ is a partial ordering on the power set of a set S $(Z, \neq)$ is a poset The directed graph is not a partial order

Which of the following statements is true?$(Z, \leq)$ is not totally orderedThe set inclusion relation $\subseteq$ is a partial ordering on the power set of a set S$(Z, \...

Pooja Khatri

3.7k views

Pooja Khatri asked Jul 13, 2018

5 votes

4 answers

2223

Test by Bikram | Mathematics | Test 2 | Question: 9
The total number of bit strings (that contain only $0$'s and $1$'s) of length $6$ that do NOT contain consecutive zeros are _______.

The total number of bit strings (that contain only $0$'s and $1$'s) of length $6$ that do NOT contain consecutive zeros are _______.

Bikram

552 views

Bikram asked May 24, 2017

2 votes

2 answers

2224

ISI 2004 MIII
Let $X$ be a nonempty set and let $\mathcal{P}(X)$ denote the collection of all subsets of $X.$ Define $\textit{f}:\textit{X$\times$ $\mathcal{P}$(X)}\rightarrow \mathbb{R}$ by $f(x,A) = \begin{cases} 1 \text{ if } x \in A & \\ 0 \text{ if } x \notin A & \end{cases}$ ... $f(x,A)+f(x,B) - f(x,A) \cdot f(x,B)$ $f(x,A)+ \mid f(x,A) - f(x,B) \mid$

Let $X$ be a nonempty set and let $\mathcal{P}(X)$ denote the collection of all subsets of $X.$ Define $\textit{f}:\textit{X$\times$ $\mathcal{P}$(X)}\rightarrow \mathbb{...

Tesla!

702 views

Tesla! asked Apr 5, 2017

1 votes

0 answers

2225

Self Doubt:Mathematical Logic
Represent these two statement in first order logic: $A)$ Only Alligators eat humans $B)$ Every Alligator eats humans Is Every represents $\equiv \exists$ and Only represents $\equiv \forall$ ?? Can we differentiate it with verb ‘eat’ and ‘eats’??

Represent these two statement in first order logic:$A)$ Only Alligators eat humans$B)$ Every Alligator eats humansIs Every represents $\equiv \exists$and Only represents ...

srestha

571 views

srestha asked May 18, 2019

0 votes

1 answer

2226

Madeeasy Discrete Maths notes
How many 5 letter word possible having atleast 2 a's ?

How many 5 letter word possible having atleast 2 a's ?

Prakhar Garg

940 views

Prakhar Garg asked Apr 9, 2019

1 votes

1 answer

2227

Kenneth Rosen Edition 6th Exercise 6.4 Question 39 (Page No. 442)
What is the generating function for the sequence of Fibonacci numbers?

What is the generating function for the sequence of Fibonacci numbers?

air1ankit

399 views

air1ankit asked Oct 9, 2017

0 votes

1 answer

2228

Kenneth Rosen Edition 7 Exercise 1.2 Question 23 (Page No. 23)
Relate to inhabitants of the island of knights and knaves created by Smullyan, where knights always tell the truth and knaves always lie. You encounter two people, $A$ and $B$. Determine, if possible, what $A$ and $B$ are if they ... what these people are, can you draw any conclusions? $A$ says We are both knaves and $B$ says nothing.

Relate to inhabitants of the island of knights and knaves created by Smullyan, where knights always tell the truth and knaves always lie. You encounter two people, $A$ an...

Pooja Khatri

940 views

Pooja Khatri asked Mar 15, 2019

0 votes

2 answers

2229

UGC NET CSE | December 2018 | Part 2 | Question: 2
Match List-I with List-II and choose the correct answer from the code given below : ... -(iii), (b)-(iv), (c)-(ii), (d)-(i) (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)

Match List-I with List-II and choose the correct answer from the code given below :$\begin{array}{|c|c|c|c|} \hline & \textbf{List I} & & \textbf{List II} ...

Arjun

2.4k views

Arjun asked Jan 2, 2019

1 votes

0 answers

2230

Ace booklet functions page:152 q.no 44
Let A, B, C are k element sets and let S be an n element set where k<=n. How many triples of functions f:A->S, g:B->S, h:C->S are there such that f, g and h are all injective and f(A) =g(B) =h(C) =?

Let A, B, C are k element sets and let S be an n element set where k<=n. How many triples of functions f:A->S, g:B->S, h:C->S are there such that f, g and h are all injec...

chandan2teja

221 views

chandan2teja asked May 27, 2019

0 votes

0 answers

2231

Rosen 7e Exercise 8.2 Questionno-26 page no-525 Recurrence Relation
What is the general form of the particular solution guaranteed to exist of the linear nonhomogeneous recurrence relation $a_n$=$6a_{n-1}$-$12a_{n-2}$+$8a_{n-3}$+F(n) if F(n)=$n^2$ F(n)=$2^n$ F(n)=$n2^n$ F(n)=$(-2)^n$ F(n)=$n^22^n$ F(n)=$n^3(-2)^n$ F(n)=3

What is the general form of the particular solution guaranteed to exist of the linear nonhomogeneous recurrence relation$a_n$=$6a_{n-1}$-$12a_{n-2}$+$8a_{n-3}$+F(n) ifF(n...

aditi19

587 views

aditi19 asked May 14, 2019

0 votes

0 answers

2232

Doubt on a math question
Chk this question https://gateoverflow.in/100202/test-series-counting $1)$Can someone verify this ans?? See if $\left ( _{0}^{6}\textrm{C} \right )$ in one set, other set will contain $\left ( _{6}^{6}\textrm{C} \right )$ elements. right?? Now why do we again need $2^{n}$ ... meaning of it?? $2)$ How $\sum_{I=0}^{n}\left ( _{i}^{n}\textrm{C} \right ).2^{n-i}=3^{n}$??

Chk this question https://gateoverflow.in/100202/test-series-counting$1)$Can someone verify this ans??See if $\left ( _{0}^{6}\textrm{C} \right )$ in one set, other set w...

srestha

224 views

srestha asked Jun 4, 2019

1 votes

1 answer

2233

ISI2018-PCB-CS3
An $n-$variable Boolean function $f:\{0,1\}^n \rightarrow \{0,1\} $ is called symmetric if its value depends only on the number of $1’s$ in the input. Let $\sigma_n $ denote the number of such functions. Calculate the value of $\sigma_4$. Derive an expression for $\sigma_n$ in terms of $n$.

An $n-$variable Boolean function $f:\{0,1\}^n \rightarrow \{0,1\} $ is called symmetric if its value depends only on the number of $1’s$ in the input. Let $\sigma_n $ d...

akash.dinkar12

519 views

akash.dinkar12 asked May 12, 2019

0 votes

3 answers

2234

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

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

Aditya Chouksey

1.2k views

Aditya Chouksey asked Dec 16, 2017

0 votes

1 answer

2235

Kenneth Rosen Edition 7 Exercise 1.2 Question 19 (Page No. 23)
Relate to inhabitants of the island of knights and knaves created by Smullyan, where knights always tell the truth and knaves always lie. You encounter two people, $A$ and $B$. Determine, if possible, what $A$ and $B$ are if they address ... can you draw any conclusions ? $A$ says At least one of us is a knave and $B$ says nothing.

Relate to inhabitants of the island of knights and knaves created by Smullyan, where knights always tell the truth and knaves always lie. You encounter two people, $A$ an...

Pooja Khatri

1.4k views

Pooja Khatri asked Mar 15, 2019

1 votes

1 answer

2236

graph theory(basic doubt)
Q.1)How many nonisomorphic simple graph are there with 6 vertices and 4 edges??

Q.1)How many nonisomorphic simple graph are there with 6 vertices and 4 edges??

BASANT KUMAR

567 views

BASANT KUMAR asked Oct 22, 2018

0 votes

0 answers

2237

Rosen 7e Exercise-8.2 Question no-23 page no-525 Recurrence Relation
Consider the nonhomogeneous linear recurrence relation $a_n$=$3a_{n-1}$+$2^n$ in the book solution is given $a_n$=$-2^{n+1}$ but I’m getting $a_n$=$3^{n+1}-2^{n+1}$

Consider the nonhomogeneous linear recurrence relation $a_n$=$3a_{n-1}$+$2^n$in the book solution is given $a_n$=$-2^{n+1}$but I’m getting $a_n$=$3^{n+1}-2^{n+1}$

aditi19

678 views

aditi19 asked May 13, 2019

0 votes

0 answers

2238

#Rosen exercise-1 ,question-71 counting
use mathematical induction to prove the sum rule for m tasks from the sum rule for two tasks.

use mathematical induction to prove the sum rule for m tasks from the sum rule for two tasks.

sandeep singh gaur

260 views

sandeep singh gaur asked May 31, 2019

12 votes

9 answers

2239

ISRO2017-22
Which one of the following Boolean expressions is NOT a tautology? $((a \rightarrow b) \wedge (b \rightarrow c)) \rightarrow (a \rightarrow c)$ $(a \leftrightarrow c) \rightarrow (\sim b\rightarrow (a\wedge c))$ $(a\wedge b \wedge c)\rightarrow (c \vee a)$ $a\rightarrow (b\rightarrow a)$

Which one of the following Boolean expressions is NOT a tautology?$((a \rightarrow b) \wedge (b \rightarrow c)) \rightarrow (a \rightarrow c)$$(a \leftrightarrow c) \rig...

sh!va

7.4k views

sh!va asked May 7, 2017

0 votes

1 answer

2240

Kenneth Rosen: Counting-13
How many bit strings with length not exceeding $n$ ,where n is a positive integer ,consist entirely of $1's?$

How many bit strings with length not exceeding $n$ ,where n is a positive integer ,consist entirely of $1's?$

rtalwar

2.5k views

rtalwar asked Oct 13, 2018

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