Recent questions and answers in Discrete Mathematics

+1 vote

1 answer

1

Pgee 2013
You have a box containing 10 black and 10 blue socks.What is the minimum number of times you need to pull out so that you have a pair of the same color?

answered 15 hours ago in Combinatory by Manas Mishra Active (2.8k points) | 19 views

0 votes

0 answers

2

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.

asked 1 day ago in Combinatory by Psnjit (207 points) | 21 views

+2 votes

1 answer

3

Rosen 7e Exercise-6.5 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?

answered 2 days ago in Combinatory by ma1999 (11 points) | 131 views

0 votes

0 answers

4

Bounded lattice
Can a countable infinite lattice be bounded?

asked 3 days ago in Set Theory & Algebra by Manoj Kumar Pandey (177 points) | 12 views

0 votes

4 answers

5

GATE 2019: Equivalent Relation
Which of the following equivalent relation of a group G? R 1 : ∀ a , b ∈ G , a R 1 b if only ∃ g ∈ G : a = g − 1 bg R 2 : ∀ a , b ∈ G , a R 2 b if only a = b –1 (a) Both R 1 and R 2 (c) R 1 (b) R 2 (d) None of these

answered 3 days ago in Set Theory & Algebra by rupesh673 (101 points) | 297 views

0 votes

1 answer

6

Set Theory
A relation R on a set of positive integers is defined by (a,b) belongs to R iff a and b are relatively prime. Which of the following is true about R? a. Symmetric and Reflexive b. Symmetric and irreflexive c.Symmetric and transitive d. Symmetric and not transitive The Ans is given as (d) but I think (b) is true. Any thoughts?

answered 3 days ago in Set Theory & Algebra by rjking7403 (33 points) | 69 views

0 votes

1 answer

7

Self doubt group theory
Is (Z+,>=) a well oerderd set ,plz explain.

answered 5 days ago in Set Theory & Algebra by PRANAB NANDY (183 points) | 34 views

+45 votes

6 answers

8

GATE2016-2-28
Consider a set $U$ of $23$ different compounds in a chemistry lab. There is a subset $S$ of $U$ of $9$ compounds, each of which reacts with exactly $3$ compounds of $U$. Consider the following statements: Each compound in U \ S reacts with an odd number ... in U \ S reacts with an even number of compounds. Which one of the above statements is ALWAYS TRUE? Only I Only II Only III None.

answered Apr 15 in Set Theory & Algebra by ShamikBanerjee Junior (669 points) | 4.4k views

0 votes

0 answers

9

Self-doubt predicate-logic
Is this statement valid: $(\exists x(P(x)\rightarrow Q(x)) )\rightarrow (\exists xP(x)\rightarrow \exists xQ(x))$

asked Apr 14 in Mathematical Logic by GATE_aspirant_2021 (15 points) | 15 views

0 votes

0 answers

10

GATE 1992
How is option (a) correct? Isn’t Universal quantifier not distributive over union/disjunction. Source: https://cse.buffalo.edu/~rapaport/191/distqfroverandor.html [closed]

asked Apr 14 in Mathematical Logic by kaveeshnyk (25 points) | 21 views

0 votes

0 answers

11

linear programming

asked Apr 12 in Mathematical Logic by shruti gupta1 (417 points) | 13 views

0 votes

0 answers

12

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 (10.7k points) | 15 views

0 votes

0 answers

13

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 (10.7k points) | 28 views

0 votes

1 answer

14

Kenneth Rosen Edition 7th Exercise 2.3 Question 69 (Page No. 155)
Find the inverse function of $f(x) = x^3 +1.$

answered Apr 11 in Set Theory & Algebra by SomeEarth Junior (629 points) | 22 views

0 votes

0 answers

15

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 one-to-one if and only if it is onto.

asked Apr 11 in Set Theory & Algebra by Pooja Khatri Boss (10.7k points) | 16 views

0 votes

0 answers

16

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 (10.7k points) | 10 views

0 votes

0 answers

17

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 (10.7k points) | 15 views

0 votes

0 answers

18

Kenneth Rosen Edition 7th Exercise 2.3 Question 68 (Page No. 155)
Draw graphs of each of these functions. $f(x) =$ $\left \lceil 3x-2 \right \rceil$ $f(x) =$ $\left \lceil 0.2x \right \rceil$ $f(x) =$ $\left \lfloor -1/x \right \rfloor$ $f(x) =$ $\left \lfloor x^2 \right \rfloor$ ... $f(x) =$ $\left \lfloor 2\left \lceil x/2 \right \rceil +1/2\right \rfloor$

asked Apr 11 in Set Theory & Algebra by Pooja Khatri Boss (10.7k points) | 12 views

0 votes

0 answers

19

Kenneth Rosen Edition 7th Exercise 2.3 Question 67 (Page No. 155)
Draw graphs of each of these functions. $f(x) =$ $\left \lfloor x+1/2 \right \rfloor$ $f(x) =$ $\left \lfloor 2x+1 \right \rfloor$ $f(x) =$ $\left \lceil x/3 \right \rceil$ $f(x) =$ $\left \lceil 1/x \right \rceil$ ... $f(x) =$ $\left \lceil \left \lfloor x-12 \right \rfloor + 1/2\right \rceil$

asked Apr 11 in Set Theory & Algebra by Pooja Khatri Boss (10.7k points) | 22 views

0 votes

0 answers

20

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 (10.7k points) | 8 views

0 votes

0 answers

21

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 (10.7k points) | 11 views

0 votes

0 answers

22

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 (10.7k points) | 15 views

0 votes

0 answers

23

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 (10.7k points) | 14 views

0 votes

0 answers

24

Kenneth Rosen Edition 7th Exercise 2.3 Question 62 (Page No. 155)
Draw the graph of the function $f(n) = 1-n^2$ from $Z$ to $Z$

asked Apr 11 in Set Theory & Algebra by Pooja Khatri Boss (10.7k points) | 4 views

0 votes

0 answers

25

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 (10.7k points) | 11 views

0 votes

0 answers

26

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 (10.7k points) | 3 views

0 votes

0 answers

27

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 (10.7k points) | 3 views

0 votes

0 answers

28

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 (10.7k points) | 7 views

0 votes

0 answers

29

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 (10.7k points) | 9 views

0 votes

0 answers

30

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 (10.7k points) | 16 views

0 votes

0 answers

31

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 (10.7k points) | 5 views

0 votes

0 answers

32

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 (10.7k points) | 13 views

0 votes

1 answer

33

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 $\left \lceil x+m \right \rceil = \left \lceil x \right \rceil +m.$

answered Apr 10 in Set Theory & Algebra by prashant jha 1 Active (5.1k points) | 16 views

0 votes

1 answer

34

Kenneth Rosen Edition 7th Exercise 2.3 Question 36 (Page No. 154)
Find $fog$ and $gof$. Where $f(x) = x^2+1$ and $g(x)= x+2$, are functions from $R$ to $R$.

answered Apr 10 in Set Theory & Algebra by SuvasishDutta (295 points) | 24 views

0 votes

0 answers

35

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 $(n-1)/2$ if $n$ is odd.

asked Apr 9 in Set Theory & Algebra by Pooja Khatri Boss (10.7k points) | 10 views

0 votes

0 answers

36

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 (10.7k points) | 20 views

0 votes

0 answers

37

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 (10.7k points) | 27 views

0 votes

0 answers

38

Kenneth Rosen Edition 7th Exercise 2.3 Question 49 (Page No. 154)
Show that if $x$ is a real number, then $x-1 < \left \lfloor x \right \rfloor <= x<= \left \lceil x \right \rceil < x+1.$

asked Apr 9 in Set Theory & Algebra by Pooja Khatri Boss (10.7k points) | 3 views

0 votes

0 answers

39

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 (10.7k points) | 17 views

0 votes

0 answers

40

Kenneth Rosen Edition 7th Exercise 2.3 Question 47 Page No. 154)
Show that $\left \lceil x-1/2 \right \rceil$ 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 (10.7k points) | 3 views

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