Recent questions in Discrete Mathematics

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1

Bounded lattice
Can a countable infinite lattice be bounded?

asked 15 hours ago in Set Theory & Algebra by Manoj Kumar Pandey (177 points) | 10 views

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2

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

asked 3 days ago in Set Theory & Algebra by Manoj Kumar Pandey (177 points) | 34 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?

asked 4 days ago in Combinatory by aditi19 Active (2.9k points) | 74 views

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4

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

asked 6 days ago in Mathematical Logic by GATE_aspirant_2021 (15 points) | 15 views

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5

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 6 days ago in Mathematical Logic by kaveeshnyk (25 points) | 17 views

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6

linear programming

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

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7

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) | 15 views

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8

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

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9

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 (10.5k points) | 16 views

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10

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) | 10 views

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11

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) | 15 views

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1 answer

12

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) | 21 views

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13

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 (10.5k points) | 11 views

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14

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 (10.5k points) | 17 views

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15

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) | 8 views

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16

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) | 11 views

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17

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

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18

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) | 14 views

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19

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 (10.5k points) | 4 views

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20

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) | 11 views

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21

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

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22

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

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23

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

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24

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

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25

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

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26

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

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27

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) | 13 views

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28

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 (10.5k points) | 10 views

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29

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

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30

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

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