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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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ISI2019MMA4
Suppose that $6$digit numbers are formed using each of the digits $1, 2, 3, 7, 8, 9$ exactly once. The number of such $6$digit numbers that are divisible by $6$ but not divisible by $9$ is equal to $120$ $180$ $240$ $360$
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May 6
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isi2019
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3
ISI2019MMA2
The number of $6$ digit positive integers whose sum of the digits is at least $52$ is $21$ $22$ $27$ $28$
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May 6
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Combinatory
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Sayan Bose
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isi2019
engineeringmathematics
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4
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
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May 2
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SPluto
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609
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72
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iitmadras
ms
writtentest
2019
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5
Discrete mathematics and its application 7th ed  Kenneth H. Rosen
Do i have to study the whole chapter Logics and Proofs in Discrete mathematics and its applications by Kenneth H. Rosen if not upto which portion should i study.
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May 1
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Mathematical Logic
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souren
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31
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discretemathematics
mathematicallogic
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6
Rosen 7e Recurrence Relation Exercise8.1 Question no25 page no511
How many bit sequences of length seven contain an even number of 0s? I'm trying to solve this using recurrence relation Is my approach correct? Let T(n) be the string having even number of 0s T(1)=1 {1} T(2)=2 {00, 11} T(3)=4 {001, ... add 0 to strings of length n1 having odd number of 0s T(n)=T(n1) Hence, we have T(n)=2T(n1)
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Apr 29
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Combinatory
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aditi19
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34
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kennethrosen
discretemathematics
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#recurrencerelations
recurrence
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7
Difference between DAG and Multistage graph
I have trouble understanding the difference between DAG and Multistage graph. I know what each of them is But I think that a multistage graph is also a DAG. Are multistage graphs a special kind of DAG?
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Apr 28
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Graph Theory
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gmrishikumar
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8
Rosen 7e Exercise8.1 Question no10 Page no511
Find a recurrence relation for the number of bit strings of length n that contain the string 01.
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Apr 28
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Combinatory
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aditi19
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kennethrosen
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#recurrencerelations
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9
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
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Set Theory & Algebra
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srestha
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23
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discretemathematics
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10
POSET self doubt
What is dual of a POSET?
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Apr 27
in
Set Theory & Algebra
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aditi19
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33
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lattice
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partialorder
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11
Made Easy Test Series:Discrete MathMathematical Logic
Consider the following first order logic statement $I)\forall x\forall yP\left ( x,y \right )$ $II)\forall x\exists yP\left ( x,y \right )$ $III)\exists x\exists yP\left ( x,y \right )$ $III)\exists x\forall yP\left ( x,y \right )$ Which one ... true , then $III),IV)$ is true $B)$ If $IV)$ is true , then $II),III)$ is true $C)$ None of these
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Apr 27
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Mathematical Logic
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srestha
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31
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mathematicallogic
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madeeasytestseries
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12
self doubt about maths practice
Where can i find only maths PYQ all branches . for practice ?
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Apr 26
in
Mathematical Logic
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paraskk
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115
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30
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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?
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Apr 25
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Set Theory & Algebra
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srestha
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14
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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aditi19
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kennethrosen
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15
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?
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Apr 22
in
Combinatory
by
Winner
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269
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84
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iiithpgee
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16
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.
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Apr 21
in
Combinatory
by
Psnjit
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211
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40
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kennethrosen
discretemathematics
permutationsandcombinations
0
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17
Bounded lattice
Can a countable infinite lattice be bounded?
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Apr 20
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Set Theory & Algebra
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Manoj Kumar Pandey
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179
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lattice
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18
Self doubt group theory
Is (Z+,>=) a well oerderd set ,plz explain.
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Apr 17
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Set Theory & Algebra
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Manoj Kumar Pandey
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179
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49
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sets
+2
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1
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19
Rosen 7e Exercise6.5 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?
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Apr 16
in
Combinatory
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aditi19
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154
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kennethrosen
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20
Discrete Mathematics [Self Doubt]
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
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15
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34
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firstorderlogic
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21
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
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kaveeshnyk
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37
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23
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discretemathematics
firstorderlogic
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votes
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22
linear programming
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Apr 12
in
Mathematical Logic
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shruti gupta1
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423
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15
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0
votes
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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
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Pooja Khatri
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11.7k
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23
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kennethrosen
discretemathematics
settheory&algebra
0
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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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30
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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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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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Apr 11
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Set Theory & Algebra
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Pooja Khatri
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kennethrosen
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settheory&algebra
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votes
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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
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Set Theory & Algebra
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kennethrosen
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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
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Pooja Khatri
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kennethrosen
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29
Kenneth Rosen Edition 7th Exercise 2.3 Question 68 (Page No. 155)
Draw graphs of each of these functions. $f(x) =$ $\left \lceil 3x2 \right \rceil$ $f(x) =$ $\left \lceil 0.2x \right \rceil$ $f(x) =$ $\left \lfloor 1/x \right \rfloor$ $f(x) =$ $\left \lfloor x^2 \right \rfloor$ ... $f(x) =$ $\left \lfloor 2\left \lceil x/2 \right \rceil +1/2\right \rfloor$
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Apr 11
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kennethrosen
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30
Kenneth Rosen Edition 7th Exercise 2.3 Question 67 (Page No. 155)
Draw graphs of each of these functions. $f(x) =$ $\left \lfloor x+1/2 \right \rfloor$ $f(x) =$ $\left \lfloor 2x+1 \right \rfloor$ $f(x) =$ $\left \lceil x/3 \right \rceil$ $f(x) =$ $\left \lceil 1/x \right \rceil$ ... $f(x) =$ $\left \lceil \left \lfloor x12 \right \rfloor + 1/2\right \rceil$
asked
Apr 11
in
Set Theory & Algebra
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11.7k
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23
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