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GATE199525b
Determine the number of positive integers $(\leq 720)$ which are not divisible by any of $2,3$ or $5.$
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Jun 6
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Set Theory & Algebra
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Arjun
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gate1995
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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 $\sum_{I=0}^{n}\left ( _{i}^{n}\textrm{C} \right ).2^{ni}=3^{n}$??
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srestha
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discretemathematics
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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
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Set Theory & Algebra
by
chandan2teja
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75
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15
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0
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0
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4
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
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Set Theory & Algebra
by
chandan2teja
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75
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17
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0
votes
0
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5
Hasse Doubt
what is the least upper bound of {a, b, c}?
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May 23
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Set Theory & Algebra
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aditi19
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40
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6
Made Easy Test Series:Lattice
The number of totally ordered set compatible to the given POSET are __________
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May 20
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Set Theory & Algebra
by
srestha
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111k
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50
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madeeasytestseries
lattice
0
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1
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7
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
in
Set Theory & Algebra
by
Shawn Frost
(
31
points)

28
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#discrete
#lattice
0
votes
2
answers
8
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
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Set Theory & Algebra
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srestha
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poset
madeeasytestseries
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9
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
(
37
points)

36
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discretemathematics
settheory&algebra
kennethrosen
0
votes
1
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10
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 $n$.
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May 12
in
Set Theory & Algebra
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akash.dinkar12
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isi2018pcbb
engineeringmathematics
discretemathematics
settheory&algebra
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descriptive
0
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1
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11
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 $S$.
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May 12
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Set Theory & Algebra
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akash.dinkar12
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isi2018pcba
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12
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
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23
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isi2018
engineeringmathematics
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groups
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13
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})
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May 10
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Set Theory & Algebra
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aditi19
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43
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kennethrosen
discretemathematics
relations
settheory&algebra
settheory
sets
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14
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
(
49
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35
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settheory&algebra
sets
discretemathematics
+1
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1
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15
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 $1$ $2$ $6$ $12$
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May 7
in
Set Theory & Algebra
by
Sayan Bose
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179
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isi2019
engineeringmathematics
discretemathematics
settheory&algebra
groups
0
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1
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16
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
in
Set Theory & Algebra
by
SPluto
Junior
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611
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80
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iitmadras
ms
writtentest
2019
0
votes
1
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17
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
in
Set Theory & Algebra
by
srestha
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111k
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23
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discretemathematics
0
votes
0
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18
POSET self doubt
What is dual of a POSET?
asked
Apr 27
in
Set Theory & Algebra
by
aditi19
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32
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lattice
selfdoubt
settheory&algebra
relations
partialorder
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1
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19
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
in
Set Theory & Algebra
by
srestha
Veteran
(
111k
points)

49
views
discretemathematics
0
votes
1
answer
20
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 $R?$
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Apr 23
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Set Theory & Algebra
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aditi19
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3.7k
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38
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kennethrosen
discretemathematics
relations
equivalenceclasses
0
votes
0
answers
21
Bounded lattice
Can a countable infinite lattice be bounded?
asked
Apr 20
in
Set Theory & Algebra
by
Manoj Kumar Pandey
(
141
points)

47
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lattice
0
votes
1
answer
22
Self doubt group theory
Is (Z+,>=) a well oerderd set ,plz explain.
asked
Apr 17
in
Set Theory & Algebra
by
Manoj Kumar Pandey
(
141
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49
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sets
0
votes
0
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23
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 $y.$
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Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
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10.7k
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views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
24
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 $x.$ ... $x.$
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Apr 11
in
Set Theory & Algebra
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Pooja Khatri
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kennethrosen
discretemathematics
settheory&algebra
0
votes
1
answer
25
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
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Set Theory & Algebra
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Pooja Khatri
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kennethrosen
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26
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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Set Theory & Algebra
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Pooja Khatri
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kennethrosen
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27
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 $(fog)^{1} = g^{1} o f^{1}.$
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Apr 11
in
Set Theory & Algebra
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Pooja Khatri
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kennethrosen
discretemathematics
settheory&algebra
0
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28
Kenneth Rosen Edition 7th Exercise 2.3 Question 69 (Page No. 155)
Find the inverse function of $f(x) = x^3 +1.$
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Apr 11
in
Set Theory & Algebra
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Pooja Khatri
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10.7k
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kennethrosen
discretemathematics
settheory&algebra
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29
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
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Pooja Khatri
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10.7k
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kennethrosen
discretemathematics
settheory&algebra
0
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30
Kenneth Rosen Edition 7th Exercise 2.3 Question 67 (Page No. 155)
Draw graphs of each of these functions. $f(x) =$ $\left \lfloor x+1/2 \right \rfloor$ $f(x) =$ $\left \lfloor 2x+1 \right \rfloor$ $f(x) =$ $\left \lceil x/3 \right \rceil$ $f(x) =$ $\left \lceil 1/x \right \rceil$ ... $f(x) =$ $\left \lceil \left \lfloor x12 \right \rfloor + 1/2\right \rceil$
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in
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Pooja Khatri
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