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Recent questions tagged settheory&algebra
Webpage for Set Theory & Algebra:
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1
Hasse Doubt
what is the least upper bound of {a, b, c}?
asked
11 hours
ago
in
Set Theory & Algebra
by
aditi19
Active
(
3.5k
points)

19
views
hassediagram
settheory&algebra
lattice
partialorder
0
votes
0
answers
2
Discrete Mathematics by Kenneth Rosen,section2.4,recursive functions
$C_{a}^{k}:\mathbb{N}^{k}\rightarrow \mathbb{N}$ I am studying discrete math from beginnings and came across this term in primitive recursive function.I don't know what $C_{a}^{k}$ means and does $\mathbb{N}$ means set of natural numbers?Someone please help me out.
asked
May 15
in
Set Theory & Algebra
by
souren
(
21
points)

32
views
discretemathematics
settheory&algebra
kennethrosen
0
votes
1
answer
3
ISI2018PCBB3
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 $n$.
asked
May 12
in
Set Theory & Algebra
by
akash.dinkar12
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(
40.6k
points)

11
views
isi2018pcbb
engineeringmathematics
discretemathematics
settheory&algebra
functions
descriptive
0
votes
1
answer
4
ISI2018PCBA4
Let $A$ and $B$ are two nonempty finite subsets of $\mathbb{Z}$, the set of all integers. Define $A+B=\{a+b:a\in A,b\in B\}$.Prove that $A+B\geq A +B 1 $, where $S$ denotes the cardinality of finite set $S$.
asked
May 12
in
Set Theory & Algebra
by
akash.dinkar12
Boss
(
40.6k
points)

16
views
isi2018pcba
engineeringmathematics
discretemathematics
settheory&algebra
descriptive
0
votes
1
answer
5
ISI2018MMA15
Let $G$ be a finite group of even order. Then which of the following statements is correct? The number of elements of order $2$ in $G$ is even The number of elements of order $2$ in $G$ is odd $G$ has no subgroup of order $2$ None of the above.
asked
May 11
in
Set Theory & Algebra
by
akash.dinkar12
Boss
(
40.6k
points)

10
views
isi2018
engineeringmathematics
discretemathematics
settheory&algebra
groups
0
votes
0
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6
Rosen 7e Exercise9.6 Question no27 page no631
What is the covering relation of the partial ordering {(A, B)  A ⊆ B} on the power set of S, where S = {a, b, c}? i'm getting R={(Ф, {a}), (Ф, {b}), (Ф, {c}), (Ф, {a, b}), (Ф, {b, c}), (Ф, {a, c}), (Ф, {a, b, c}), ({a}, {a, b}), ({a}, {a, c}), ({b}, ... b, c}), ({c}, {a, c}), ({c}, {b, c}), ({a, b}, {a, b, c}), ({a, c}, {a, b, c})({b, c}, {a, b, c})
asked
May 10
in
Set Theory & Algebra
by
aditi19
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3.5k
points)

40
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kennethrosen
discretemathematics
relations
settheory&algebra
settheory
sets
+1
vote
0
answers
7
Which Statement is correct for the given sets statements
If A, B, C are three sets then which of the following is TRUE ? If ( A ∩ C ) = ( B ∩ C ) then A = B If ( A ∪ C ) = ( B ∪ C ) then A = B If ( A 𝜟 C ) = ( B 𝜟 C ) then A = B If ( A – C ) = ( B – C ) then A = B
asked
May 10
in
Set Theory & Algebra
by
pranay91331
(
43
points)

25
views
settheory&algebra
sets
discretemathematics
0
votes
1
answer
8
ISI2019MMA30
Consider the function $h$ defined on $\{0,1,…….10\}$ with $h(0)=0, \: h(10)=10 $ and $2[h(i)h(i1)] = h(i+1) – h(i) \: \text{ for } i = 1,2, \dots ,9.$ Then the value of $h(1)$ is $\frac{1}{2^91}\\$ $\frac{10}{2^9+1}\\$ $\frac{10}{2^{10}1}\\$ $\frac{1}{2^{10}+1}$
asked
May 7
in
Calculus
by
Sayan Bose
Loyal
(
6.9k
points)

319
views
isi2019
engineeringmathematics
discretemathematics
settheory&algebra
functions
+1
vote
1
answer
9
ISI2019MMA19
Let $G =\{a_1,a_2, \dots ,a_{12}\}$ be an Abelian group of order $12$ . Then the order of the element $ ( \prod_{i=1}^{12} a_i)$ is $1$ $2$ $6$ $12$
asked
May 7
in
Set Theory & Algebra
by
Sayan Bose
Loyal
(
6.9k
points)

160
views
isi2019
engineeringmathematics
discretemathematics
settheory&algebra
groups
0
votes
0
answers
10
POSET self doubt
What is dual of a POSET?
asked
Apr 27
in
Set Theory & Algebra
by
aditi19
Active
(
3.5k
points)

31
views
lattice
selfdoubt
settheory&algebra
relations
partialorder
0
votes
0
answers
11
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
(
11.7k
points)

23
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
12
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
(
11.7k
points)

30
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
1
answer
13
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
(
11.7k
points)

28
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
14
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
(
11.7k
points)

17
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
15
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
(
11.7k
points)

23
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
1
answer
16
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
(
11.7k
points)

28
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
17
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
(
11.7k
points)

19
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
18
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
(
11.7k
points)

23
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
19
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
(
11.7k
points)

12
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
20
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
(
11.7k
points)

19
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
21
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
(
11.7k
points)

15
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
22
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
(
11.7k
points)

20
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
23
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
(
11.7k
points)

5
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
24
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
(
11.7k
points)

18
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
25
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
(
11.7k
points)

5
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
26
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
(
11.7k
points)

3
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
27
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
(
11.7k
points)

9
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
28
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
(
11.7k
points)

9
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
29
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
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(
11.7k
points)

17
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
30
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
(
11.7k
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9
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kennethrosen
discretemathematics
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