The Gateway to Computer Science Excellence
For all GATE CSE Questions
Toggle navigation
GATE Overflow
Facebook Login
or
Email or Username
Password
Remember
Login
Register

I forgot my password
Activity
Questions
Unanswered
Tags
Subjects
Users
Ask
Prev
Blogs
New Blog
Exams
First time here? Checkout the
FAQ
!
x
×
Close
Use the google search bar on side panel. It searches through all previous GATE/other questions. For hardcopy of previous year questions please see
here
Recent questions tagged kennethrosen
0
votes
1
answer
1
Rosen 7e Exercise6.5 question 45.b page 433
How many ways can n books be placed on k distinguishable shelves if no two books are the same, and the positions of the books on the shelves matter?
asked
3 days
ago
in
Combinatory
by
aditi19
Active
(
2.9k
points)

22
views
kennethrosen
discretemathematics
permutationsandcombinations
combinatory
0
votes
0
answers
2
Kenneth Rosen Edition 7th Exercise 2.3 Question 74 (Page No. 155)
Prove or disprove each of these statements about the floor and ceiling functions. $\left \lfloor \left \lceil x \right \rceil \right \rfloor = \left \lceil x \right \rceil$ for all real numbers $x.$ ... $x$ and $y.$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

13
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
3
Kenneth Rosen Edition 7th Exercise 2.3 Question 73 (Page No. 155)
Prove or disprove each of these statements about the floor and ceiling functions. $\left \lceil \left \lfloor x \right \rfloor \right \rceil = \left \lfloor x \right \rfloor$ for all real number $x.$ ... $x.$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

22
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
4
Kenneth Rosen Edition 7th Exercise 2.3 Question 72 (Page No. 155)
Suppose that $f$ is a function from $A$ to $B$, where $A$ and $B$ are finite sets with $A=B$. Show that $f$ is onetoone if and only if it is onto.
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

13
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
5
Kenneth Rosen Edition 7th Exercise 2.3 Question 71 (Page No. 155)
Let $S$ be a subset of a universal set $U$. The characteristic function $f_{s}$ of $S$ is the function from $U$ to the set $\left \{ 0,1 \right \}$ such that $f_{S}(x)=1$ if $x$ belongs to $S$ and $f_S(x)=0$ if $x$ does not belong to $S$. Let $A$ ... $f_{A \oplus B}(x) = f_{A}(x) + f_{B}(x) 2 f_{A}(x) f_{B}(x) $
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

8
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
6
Kenneth Rosen Edition 7th Exercise 2.3 Question 70 (Page No. 155)
Suppose that $f$ is an invertible function from $Y$ to $Z$ and $g$ is an invertible function from $X$ to $Y$. Show that the inverse of the composition $fog$ is given by $(fog)^{1} = g^{1} o f^{1}.$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

13
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
1
answer
7
Kenneth Rosen Edition 7th Exercise 2.3 Question 69 (Page No. 155)
Find the inverse function of $f(x) = x^3 +1.$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

19
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
8
Kenneth Rosen Edition 7th Exercise 2.3 Question 68 (Page No. 155)
Draw graphs of each of these functions. $f(x) =$ $\left \lceil 3x2 \right \rceil$ $f(x) =$ $\left \lceil 0.2x \right \rceil$ $f(x) =$ $\left \lfloor 1/x \right \rfloor$ $f(x) =$ $\left \lfloor x^2 \right \rfloor$ ... $f(x) =$ $\left \lfloor 2\left \lceil x/2 \right \rceil +1/2\right \rfloor$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

9
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
9
Kenneth Rosen Edition 7th Exercise 2.3 Question 67 (Page No. 155)
Draw graphs of each of these functions. $f(x) =$ $\left \lfloor x+1/2 \right \rfloor$ $f(x) =$ $\left \lfloor 2x+1 \right \rfloor$ $f(x) =$ $\left \lceil x/3 \right \rceil$ $f(x) =$ $\left \lceil 1/x \right \rceil$ ... $f(x) =$ $\left \lceil \left \lfloor x12 \right \rfloor + 1/2\right \rceil$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

17
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
10
Kenneth Rosen Edition 7th Exercise 2.3 Question 66 (Page No. 155)
Draw the graph of the function $f(n) =$ $\left \lceil x \right \rceil +\left \lceil x/2 \right \rceil$ from $R$ to $R$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

5
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
11
Kenneth Rosen Edition 7th Exercise 2.3 Question 65 (Page No. 155)
Draw the graph of the function $f(n) =$\left \lfloor x \right \rfloor +\left \lfloor x/2 \right \rfloor$ from $R$ to $R$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

8
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
12
Kenneth Rosen Edition 7th Exercise 2.3 Question 64 (Page No. 155)
Draw the graph of the function $f(n) =$\left \lfloor x/2 \right \rfloor$ from $R$ to $R$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

11
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
13
Kenneth Rosen Edition 7th Exercise 2.3 Question 63 (Page No. 155)
Draw the graph of the function $f(n) =$\left \lfloor 2x \right \rfloor$ from $R$ to $R$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

9
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
14
Kenneth Rosen Edition 7th Exercise 2.3 Question 62 (Page No. 155)
Draw the graph of the function $f(n) = 1n^2$ from $Z$ to $Z$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

4
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
15
Kenneth Rosen Edition 7th Exercise 2.3 Question 61 (Page No. 155)
Data are transmitted over a particular Ethernet network in blocks of $1500$ octets (blocks of $8$ bits). How many blocks are required to transmit the following amounts of data over this Ethernet network? (Note that a byte is a synonym ... $1.544$ $\text{megabytes}$ of data $45.3$ $\text{megabytes of}$ data
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

7
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
16
Kenneth Rosen Edition 7th Exercise 2.3 Question 60 (Page No. 155)
How many ATM cells (described in Example 28) can be transmitted in $10$ seconds over a link operating at the following rates? $128$ kilobits per second ($1$ kilobit= $1000$ bits) $300$ kilobits per second $1$ megabit per second ($1$ megabit=$1,000,000$ bits)
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

3
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
17
Kenneth Rosen Edition 7th Exercise 2.3 Question 59 (Page No. 155)
How many bytes are required to encode $n$ bits of data where $n$ equals $7$ $17$ $1001$ $28800$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

3
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
18
Kenneth Rosen Edition 7th Exercise 2.3 Question 58 (Page No. 154)
How many bytes are required to encode $n$ bits of data where $n$ equals $4$ $10$ $500$ $3000$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

7
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
19
Kenneth Rosen Edition 7th Exercise 2.3 Question 57 (Page No. 154)
Let $a$ and $b$ be real numbers with $a<b$. Use the floor and / or ceiling functions to express the number of integers $n$ that satisfy the inequality $a<n<b.$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

9
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
20
Kenneth Rosen Edition 7th Exercise 2.3 Question 56 (Page No. 154)
Let $a$ and $b$ be real numbers with $a<b$. Use the floor and / or ceiling functions to express the number of integers $n$ that satisfy the inequality $a≤n≤b$.
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

12
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
21
Kenneth Rosen Edition 7th Exercise 2.3 Question 55 (Page No. 154)
The function INT is found on some calculators, where INT$(x)$ = $\left \lfloor x \right \rfloor$ when $x$ nonnegative real number and INT$(x)$ = $\left \lceil x \right \rceil$ when x is a negative real number. Show that this INT function satisfies the identity INT$(x)$=$$ INT$(x)$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

5
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
22
Kenneth Rosen Edition 7th Exercise 2.3 Question 54 (Page No. 154)
Prove that if $x$ is a reall number , then $\left \lfloor x \right \rfloor =  \left \lceil x \right \rceil$ and$\left \lceil x \right \rceil = \left \lfloor x \right \rfloor$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

10
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
23
Kenneth Rosen Edition 7th Exercise 2.3 Question 53 (Page No. 154)
Prove that if $n$ is an integer, then $\left \lfloor n/2 \right \rfloor = n/2$ if $n$ is even and $(n1)/2$ if $n$ is odd.
asked
Apr 9
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

10
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
24
Kenneth Rosen Edition 7th Exercise 2.3 Question 52 (Page No. 154)
Show that if $x$ is a real number and $n$ is an integer, then $x<=n$ if and only if $\left \lceil x \right \rceil <=n$ $n<=x$ if and only if $ n<=\left \lfloor x \right \rfloor $
asked
Apr 9
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

16
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
25
Kenneth Rosen Edition 7th Exercise 2.3 Question 51 (Page No. 154)
Show that if $x$ is a real number and $n$ is an integer, then $x<n$ if and only if $\left \lfloor x \right \rfloor < n$ $n<x$ if and only if $ n<=\left \lfloor x \right \rfloor $
asked
Apr 9
in
Mathematical Logic
by
Pooja Khatri
Boss
(
10.5k
points)

18
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
1
answer
26
Kenneth Rosen Edition 7th Exercise 2.3 Question 50 (Page No. 154)
Show that if $x$ is a real number, and $m$ is an integer, then $\left \lceil x+m \right \rceil = \left \lceil x \right \rceil +m.$
asked
Apr 9
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

16
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
27
Kenneth Rosen Edition 7th Exercise 2.3 Question 49 (Page No. 154)
Show that if $x$ is a real number, then $x1 < \left \lfloor x \right \rfloor <= x<= \left \lceil x \right \rceil < x+1.$
asked
Apr 9
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

3
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
28
Kenneth Rosen Edition 7th Exercise 2.3 Question 48 (Page No. 154)
Show that if $x$ is a real number, then $\left \lceil x \right \rceil  \left \lfloor x \right \rfloor =1$ if $x$ is not an integer and $\left \lceil x \right \rceil  \left \lfloor x \right \rfloor =0$ if $x$ is an integer.
asked
Apr 9
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

12
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
29
Kenneth Rosen Edition 7th Exercise 2.3 Question 47 Page No. 154)
Show that $\left \lceil x1/2 \right \rceil$ is the closest integer to the number $x$,except when $x$ is midway between two integers, when it is the smaller of these two integers
asked
Apr 9
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

3
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
30
Kenneth Rosen Edition 7th Exercise 2.3 Question 46 (Page No. 154)
Show that $\left \lfloor x+1/2 \right \rfloor$ is the closest integer to the number $x$,except when $x$ is midway between two integers, when it is the larger of these two integers
asked
Apr 9
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.5k
points)

10
views
kennethrosen
discretemathematics
settheory&algebra
Page:
1
2
3
4
5
6
...
21
next »
Quick search syntax
tags
tag:apple
author
user:martin
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
Recent Posts
GATE score validity queries.
How to prepare for IISC Interdisciplinary Mathematical Sciences Interview
GO Hardcopy for GATE 2020
How to prepare for BARC interview
IIIT H
Follow @csegate
Recent questions tagged kennethrosen
Recent Blog Comments
THey removed it this year... I did not check it,...
even though i am not going for iiit , can you...
I don't think IIITD requires any codechef...
Will apply for IIITB. IIIT D requires a codechef...
Go for it. Nobody cares once you join a good IIT...
50,083
questions
53,206
answers
184,555
comments
70,426
users