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Doubt on a math question
Chk this question https://gateoverflow.in/100202/testseriescounting $1)$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 $\sum_{I=0}^{n}\left ( _{i}^{n}\textrm{C} \right ).2^{ni}=3^{n}$??
asked
Jun 4, 2019
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Set Theory & Algebra
by
srestha
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119k
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53
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discretemathematics
settheory&algebra
+1
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0
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2
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) =?
asked
May 27, 2019
in
Set Theory & Algebra
by
chandan2teja
(
147
points)

29
views
0
votes
0
answers
3
Ace workbook lattice concept
If X is minimum element of S then X is related to y for all y belongs to S. Let [S;R] be a poset. If every non empty subset of S has a minimum element then a) S is Totally ordered set b) S is bounded set. C) S is complemented ... then 1 will be part of every non empty subset of S. Is this correct way of interpreting the question. If not can you please elaborate it
asked
May 26, 2019
in
Set Theory & Algebra
by
chandan2teja
(
147
points)

32
views
0
votes
2
answers
4
Hasse Doubt
what is the least upper bound of {a, b, c}?
asked
May 23, 2019
in
Set Theory & Algebra
by
aditi19
Loyal
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5.2k
points)

135
views
hassediagram
settheory&algebra
lattice
partialorder
+1
vote
1
answer
5
Made Easy Test Series:Lattice
The number of totally ordered set compatible to the given POSET are __________
asked
May 20, 2019
in
Set Theory & Algebra
by
srestha
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119k
points)

118
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madeeasytestseries
lattice
0
votes
1
answer
6
Discrete mathematics #TEST_BOOK
I Have doubt about the language. Is it asking about the sum of elements if we make the GBL set for the given lattice .
asked
May 20, 2019
in
Set Theory & Algebra
by
Shawn Frost
(
31
points)

40
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#discrete
#lattice
0
votes
2
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7
Made Easy Test Series:Discrete MathematicsPoset
Consider the following Posets: $I)\left ( \left \{ 1,2,5,7,10,14,35,70 \right \},\leq \right )$ $II)\left ( \left \{ 1,2,3,6,14,21,42 \right \},/ \right )$ $III)\left ( \left \{ 1,2,3,6,11,22,33,66 \right \},/ \right )$ Which of the above poset are isomorphic to $\left ( P\left ( S \right ),\subseteq \right )$ where $S=\left \{ a,b,c \right \}?$
asked
May 18, 2019
in
Set Theory & Algebra
by
srestha
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119k
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83
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poset
madeeasytestseries
discretemathematics
0
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0
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8
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, 2019
in
Set Theory & Algebra
by
souren
(
37
points)

59
views
discretemathematics
settheory&algebra
kennethrosen
+1
vote
1
answer
9
ISI2018PCBCS3
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, 2019
in
Set Theory & Algebra
by
akash.dinkar12
Boss
(
42.5k
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45
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isi2018pcbcs
engineeringmathematics
discretemathematics
settheory&algebra
functions
descriptive
0
votes
1
answer
10
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 $\mid A+B \mid \geq \mid A \mid + \mid B \mid 1 $, where $\mid S \mid$ denotes the cardinality of finite set $S$.
asked
May 12, 2019
in
Set Theory & Algebra
by
akash.dinkar12
Boss
(
42.5k
points)

45
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isi2018pcba
settheory&algebra
descriptive
0
votes
1
answer
11
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, 2019
in
Set Theory & Algebra
by
akash.dinkar12
Boss
(
42.5k
points)

96
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isi2018mma
engineeringmathematics
discretemathematics
settheory&algebra
grouptheory
0
votes
0
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12
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, 2019
in
Set Theory & Algebra
by
aditi19
Loyal
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5.2k
points)

75
views
kennethrosen
discretemathematics
relations
settheory&algebra
sets
+1
vote
0
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13
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, 2019
in
Set Theory & Algebra
by
pranay91331
(
73
points)

74
views
settheory&algebra
sets
discretemathematics
+1
vote
1
answer
14
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, 2019
in
Set Theory & Algebra
by
Sayan Bose
Loyal
(
7.4k
points)

247
views
isi2019mma
engineeringmathematics
discretemathematics
settheory&algebra
grouptheory
0
votes
1
answer
15
IIT Madras MS written test 2019
Which of the following infinite sets have the same cardinality? $\mathbb{N}$ : Set of Natural numbers $\mathbb{E}$ : Set of Even numbers $\mathbb{Q}$ : Set of Rational numbers $\mathbb{R}$ : Set of Real numbers $\mathbb{N}$ and $\mathbb{E}$ $\mathbb{Q}$ and $\mathbb{R}$ $\mathbb{R}$ and $\mathbb{N}$ None of the above
asked
May 2, 2019
in
Set Theory & Algebra
by
SPluto
Junior
(
677
points)

93
views
iitmadras
ms
writtentest
2019
0
votes
2
answers
16
SelfDoubt:Mathematical logic
“Every asymmetric relation is antisymmetric” Is this statement is True or False? I think it is false, because asymmetric relation never allows loops and antisymmetric relation allows loops. Am I not correct?
asked
Apr 27, 2019
in
Set Theory & Algebra
by
srestha
Veteran
(
119k
points)

38
views
discretemathematics
0
votes
0
answers
17
POSET self doubt
What is dual of a POSET?
asked
Apr 27, 2019
in
Set Theory & Algebra
by
aditi19
Loyal
(
5.2k
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69
views
lattice
selfdoubt
settheory&algebra
relations
partialorder
0
votes
1
answer
18
Allen Career Institute: Discrete Math
Let $f : A \rightarrow B$ be a bijection and let $E,F$ be subjects of $A$, Now, we consider the following statements about the function $f :$ $P : f(E \cup F) = f (E) \cup f(F)$ ... None of $P$ and $Q$ is correct I thought $Q$ is true, but answer is both true. Is both true because of bijective function or ans given incorrect?
asked
Apr 25, 2019
in
Set Theory & Algebra
by
srestha
Veteran
(
119k
points)

58
views
discretemathematics
0
votes
1
answer
19
Rosen 7e Exercise9.5 Question no9 page no615
Suppose that $A$ is a nonempty set, and $f$ is a function that has $A$ as its domain. Let $R$ be the relation on $A$ consisting of all ordered pairs $(x, y)$ such that $f (x)=f (y)$ $a)$ Show that $R$ is an equivalence relation on $A$ $b)$ What are the equivalence classes of $R?$
asked
Apr 23, 2019
in
Set Theory & Algebra
by
aditi19
Loyal
(
5.2k
points)

54
views
kennethrosen
discretemathematics
relations
equivalenceclasses
0
votes
0
answers
20
Bounded lattice
Can a countable infinite lattice be bounded?
asked
Apr 20, 2019
in
Set Theory & Algebra
by
Manoj Kumar Pandey
(
281
points)

70
views
lattice
0
votes
1
answer
21
Self doubt group theory
Is (Z+,>=) a well oerderd set ,plz explain.
asked
Apr 17, 2019
in
Set Theory & Algebra
by
Manoj Kumar Pandey
(
281
points)

59
views
sets
0
votes
0
answers
22
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, 2019
in
Set Theory & Algebra
by
Pooja Khatri
Boss
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10.9k
points)

25
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
23
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, 2019
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.9k
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35
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kennethrosen
discretemathematics
settheory&algebra
0
votes
1
answer
24
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.
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Apr 11, 2019
in
Set Theory & Algebra
by
Pooja Khatri
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10.9k
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40
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kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
25
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) $
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Apr 11, 2019
in
Set Theory & Algebra
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Pooja Khatri
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10.9k
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19
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kennethrosen
discretemathematics
settheory&algebra
0
votes
0
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26
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, 2019
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.9k
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25
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kennethrosen
discretemathematics
settheory&algebra
+1
vote
2
answers
27
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, 2019
in
Set Theory & Algebra
by
Pooja Khatri
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10.9k
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51
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kennethrosen
discretemathematics
settheory&algebra
0
votes
0
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28
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, 2019
in
Set Theory & Algebra
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Pooja Khatri
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10.9k
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21
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kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
29
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, 2019
in
Set Theory & Algebra
by
Pooja Khatri
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10.9k
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26
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kennethrosen
discretemathematics
settheory&algebra
0
votes
0
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30
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, 2019
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.9k
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13
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settheory&algebra
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