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Recent questions and answers in Mathematical Logic
+6
votes
6
answers
1
GATE201935
Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z \mid x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z \mid w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ ... Set of all positive integers $S3:$ Set of all integers Which of the above sets satisfy $\varphi$? S1 and S2 S1 and S3 S2 and S3 S1, S2 and S3
answered
5 days
ago
in
Mathematical Logic
by
habedo007
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2.4k
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gate2019
engineeringmathematics
discretemathematics
mathematicallogic
firstorderlogic
+32
votes
7
answers
2
GATE20021.8
"If $X$ then $Y$ unless $Z$" is represented by which of the following formulas in prepositional logic? ("$\neg$" is negation, "$\land$" is conjunction, and "$\rightarrow$" is implication) $(X\land \neg Z) \rightarrow Y$ $(X \land Y) \rightarrow \neg Z$ $X \rightarrow(Y\land \neg Z)$ $(X \rightarrow Y)\land \neg Z$
answered
6 days
ago
in
Mathematical Logic
by
Navneet Singh Tomar
Junior
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595
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4.3k
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gate2002
mathematicallogic
normal
propositionallogic
0
votes
2
answers
3
solution of rosen
can anyone has the soft copy of kenneth h rosen solutions?
answered
Nov 11
in
Mathematical Logic
by
Ram Swaroop
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4.4k
points)

394
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+2
votes
3
answers
4
Rosen chapter 5.5 question 50
How many ways are there to distribute 5 distinguishable objects into three indistinguishable boxes?
answered
Nov 9
in
Mathematical Logic
by
SaurabhKatkar
(
77
points)

242
views
+9
votes
4
answers
5
GATE19893v
Answer the following: Which of the following wellformed formulas are equivalent? $P \rightarrow Q$ $\neg Q \rightarrow \neg P$ $\neg P \vee Q$ $\neg Q \rightarrow P$
answered
Oct 8
in
Mathematical Logic
by
vupadhayayx86
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1.5k
points)

600
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gate1989
normal
mathematicallogic
propositionallogic
+23
votes
5
answers
6
GATE200923
Which one of the following is the most appropriate logical formula to represent the statement? "Gold and silver ornaments are precious". The following notations are used: $G(x): x$ is a gold ornament $S(x): x$ is a silver ornament $P(x): x$ ... $\exists x((G(x) \wedge S(x)) \implies P(x))$ $\forall x((G(x) \vee S(x)) \implies P(x))$
answered
Sep 17
in
Mathematical Logic
by
manikantsharma
(
411
points)

1.8k
views
gate2009
mathematicallogic
easy
firstorderlogic
0
votes
0
answers
7
CMI2019B5
In the land of Twitter, there are two kinds of people: knights (also called outragers), who always tell the truth, and knaves (also called trolls), who always lie. It so happened that a person with handle @anand tweeted something offensive. It was not known whether @anand was ... $ 1$ : @anand once claimed that I was a knave. Chitra : Are you by any chance @anand? Suspect $1$ : Yes.
asked
Sep 13
in
Mathematical Logic
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gatecse
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knightsknaves
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0
votes
1
answer
8
Kenneth Rosen Edition 7th Exercise 1.6 Question 30 (Page No. 80)
Use resolution to show the hypotheses “Allen is a bad boy or Hillary is a good girl” and “Allen is a good boy or David is happy” imply the conclusion “Hillary is a good girl or David is happy.”
answered
Sep 7
in
Mathematical Logic
by
tejamach
(
11
points)

17
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
+1
vote
1
answer
9
How do I prepare Engineering Mathematics for Gate CS?
Good Morning, I want to start Engineering Mathematics and need help from you to know where to start and what would be the best sequence to complete the whole subject?
answered
Sep 4
in
Mathematical Logic
by
Akashniranjan
(
11
points)

529
views
preparation
general
+1
vote
2
answers
10
UGCNETJune2013II40
The truth value of the statements: $\exists ! xP(x) \rightarrow \exists xP(x) \text{ and } \exists ! x \rceil P(x) \rightarrow \rceil \forall xP(x)$, (where the notation $\exists ! x P(x)$ denotes the proposition “There exists a unique $x$ such that $P(x)$ is true”) are: True and False False and True False and False True and True
answered
Aug 31
in
Mathematical Logic
by
GoalSet1
(
191
points)

564
views
ugcnetjune2013ii
+2
votes
2
answers
11
Find the number of into functions
answered
Aug 26
in
Mathematical Logic
by
Lakshman Patel RJIT
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53.4k
points)

1.3k
views
+1
vote
1
answer
12
Knights , Knaves , spy
answered
Aug 24
in
Mathematical Logic
by
Kushagra गुप्ता
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1.1k
points)

99
views
+27
votes
3
answers
13
GATE201431
Consider the following statements: P: Good mobile phones are not cheap Q: Cheap mobile phones are not good L: P implies Q M: Q implies P N: P is equivalent to Q Which one of the following about L, M, and N is CORRECT? Only L is TRUE. Only M is TRUE. Only N is TRUE. L, M and N are TRUE.
answered
Aug 16
in
Mathematical Logic
by
sohailkhan
(
67
points)

2.5k
views
gate20143
mathematicallogic
easy
propositionallogic
0
votes
1
answer
14
recurrence relation
Which recurrence relation satisfy the sequence: 2, 3, 4, . . ., for n ≥ 1. A ) T(N) = 2 T(N1)  T(N2) B)T(N) = T(N1) + T(N2) C)T(N) = N+1 D) None of these
answered
Aug 8
in
Mathematical Logic
by
Rohit Suryanarayan
(
15
points)

465
views
recurrence
+55
votes
4
answers
15
GATE200333
Consider the following formula and its two interpretations \(I_1\) and \(I_2\). \(\alpha: (\forall x)\left[P_x \Leftrightarrow (\forall y)\left[Q_{xy} \Leftrightarrow \neg Q_{yy} \right]\right] \Rightarrow (\forall x)\left[\neg P_x\right]\) \(I_1\) : Domain: the set of ... , \(I_1\) does not Neither \(I_1\) nor \(I_2\) satisfies \(\alpha\) Both \(I_1\) and \(I_2\) satisfies \(\alpha\)
answered
Aug 6
in
Mathematical Logic
by
MRINMOY_HALDER
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2.9k
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4.3k
views
gate2003
mathematicallogic
difficult
firstorderlogic
0
votes
1
answer
16
Probability
Prabha is working in a software company. Her manager is running a dinner for those employees having atleast one son. If Prabha is invited to the dinner and everyone knows she has two children. What is the probability that they are both boys?
answered
Jul 20
in
Mathematical Logic
by
bankeshk
(
59
points)

50
views
probability
engineeringmathematics
conditionalprobability
+1
vote
1
answer
17
relation
A binary relation R on Z × Z is defined as follows: (a, b) R (c, d) iff a = c or b = d Consider the following propositions: 1. R is reflexive. 2. R is symmetric. 3. R is antisymmetric. Which one of the following statements is True? A Both 1 and 2 are true B 1 is true and 2 is false C 1 is false and 3 is true D Both 2 and 3 are true
answered
Jul 12
in
Mathematical Logic
by
mohan123
Active
(
1.2k
points)

71
views
+4
votes
2
answers
18
UGCNETJune2019II8
Match ListI with ListII: ... )  (iv); (b)  (i); (c)  (iii); (d)  (ii) (a)  (iv); (b)  (iii); (c)  (i); (d)  (ii)
answered
Jul 7
in
Mathematical Logic
by
Lakshmikanta
(
55
points)

155
views
ugcnetjune2019ii
propositionallogic
+4
votes
2
answers
19
UGCNETJune2019II6
Which of the following is principal conjunctive normal form for $[(p\vee q)\wedge\ \rceil p \rightarrow \rceil q ]$ ? $p\ \vee \rceil q$ $p \vee q $ $\rceil p \vee q$ $\rceil p\ \vee \rceil q$
answered
Jul 7
in
Mathematical Logic
by
Satbir
Boss
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20.7k
points)

229
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ugcnetjune2019ii
propositionallogic
0
votes
1
answer
20
MadeEasy Test Series: Probability
How to get the idea that we have to use Binomial distribution or Hypergeometric Distribution. I know that if the probability is not changing(i.e with replacement) then we go Binomial otherwise Hypergeometric. But in question, it is not indicating ... So is there any by default approach that we have to use Binomial if nothing is a mention about a replacement.
answered
Jun 13
in
Mathematical Logic
by
vizzard110
(
279
points)

37
views
madeeasytestseries
probability
binomialdistribution
+4
votes
1
answer
21
TIFR2017B6
Consider the First Order Logic (FOL) with equality and suitable function and relation symbols. Which of the following is FALSE? Partial orders cannot be axiomatized in FOL FOL has a complete proof system Natural numbers cannot be axiomatized in FOL Real numbers cannot be axiomatized in FOL Relational numbers cannot be axiomatized in FOL
answered
Jun 8
in
Mathematical Logic
by
Arjun
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(
423k
points)

202
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tifr2017
firstorderlogic
normal
0
votes
1
answer
22
GATE198814i
Consider the following wellformed formula: $\exists x \forall y [ \neg \: \exists z [ p (y, z) \wedge p (z, y) ] \equiv p(x,y)]$ Express the above wellformed formula in clausal form.
answered
Jun 7
in
Mathematical Logic
by
Arjun
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423k
points)

168
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gate1988
descriptive
firstorderlogic
clausalform
nongate
+1
vote
2
answers
23
UGCNETDec2015II6
Which of the following arguments are not valid ? "If Gora gets the job and works hard, then he will be promoted. if Gora gets promotion, then he will be happy. He will not be happy, therefore, either he will not get the job or he will not work hard." "Either Puneet is not ... $n^2 > 1$, then $n>1$. a and c b and c a,b, and c a and b
answered
Jun 6
in
Mathematical Logic
by
Satbir
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20.7k
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1.5k
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ugcnetdec2015ii
discretemathematics
mathematicallogic
+2
votes
1
answer
24
Mathematical Logic Ques:Self doubt
“Not every satisfiable logic is valid” Representation of it will be $1)\sim \left ( \forall S(x)\rightarrow V(x) \right )$ or $2)\sim \left ( \forall S(x)\vee V(x) \right )$ Among $1)$ and $2)$, which one is correct? and why?
answered
Jun 4
in
Mathematical Logic
by
Satbir
Boss
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20.7k
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154
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discretemathematics
mathematicallogic
+26
votes
2
answers
25
GATE200541
What is the first order predicate calculus statement equivalent to the following? "Every teacher is liked by some student" $∀(x)\left[\text{teacher}\left(x\right) → ∃(y) \left[\text{student}\left(y\right) → \text{likes}\left(y,x\right)\right]\right]$ ...
answered
Jun 3
in
Mathematical Logic
by
MRINMOY_HALDER
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2.9k
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2.9k
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gate2005
mathematicallogic
easy
firstorderlogic
+2
votes
1
answer
26
Doubt on GATE Question
Read the statements: All women are entrepreneurs. Some women are doctors. Which of the following conclusions can be logically inferred from the above statements? All women are doctors All doctors are entrepreneurs All entrepreneurs are women Some entrepreneurs are doctors ... Is it because , if we make set of doctor as 0, then All doctors are entrepreneurs is meaningless.
answered
Jun 1
in
Mathematical Logic
by
Hirak
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3.5k
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60
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discretemathematics
mathematicallogic
+1
vote
1
answer
27
Mathematical Logic: Doubt on meaning of statement
The notation $\exists ! x P(x)$ denotes the proposition there exists a unique $x$ such that $P(x)$ ... What will be answer here?? Is the assumption only for left hand side and not right hand side??
answered
May 31
in
Mathematical Logic
by
Satbir
Boss
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20.7k
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82
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mathematicallogic
discretemathematics
+15
votes
4
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28
TIFR2011A1
If either wages or prices are raised, there will be inflation. If there is inflation, then either the government must regulate it or the people will suffer. If the people suffer, the government will be unpopular. Government will not be unpopular. Which of the ... are not raised Prices are not raised If the inflation is not regulated, then the prices are not raised Wages are not raised
answered
May 31
in
Mathematical Logic
by
srestha
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117k
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tifr2011
mathematicallogic
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logicalreasoning
+9
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4
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29
TIFR2010A4
If the bank receipt is forged, then Mr. M is liable. If Mr. M is liable, he will go bankrupt. If the bank will loan him money, he will not go bankrupt. The bank will loan him money. Which of the following can be concluded from the above statements? Mr. M is liable The receipt is not forged Mr. M will go bankrupt The bank will go bankrupt None of the above
answered
May 31
in
Mathematical Logic
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srestha
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117k
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514
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tifr2010
logicalreasoning
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0
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1
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30
Kenneth Rosen Edition 7th Exercise 1.4 Question 47 (Page No. 56)
Establish these logical equivalences, where $x$ does not occur as a free variable in $A$. Assume that the domain is nonempty. $(\forall x P(x)) \wedge A \equiv \forall x (P(x) \wedge A)$ $(\exists x P(x)) \wedge A \equiv \exists x (P(x) \wedge A)$
answered
May 30
in
Mathematical Logic
by
srestha
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117k
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40
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kennethrosen
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0
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31
Descrete Mathematic ACE Text Book Practice Question #16
A women's health clinic has four doctors and each patient is assigned to one of them. If a patient givs birth btween 8 am and 4 pm, then her chance of being attended by her assigned doctor is 3/4, otherwise it is 1/4. What is the probability that ... is attended by the assigned doctor when she gives birth? (A) 25/144 (B) 5/12 (C) 7/12 (D) 1/12
[closed]
asked
May 30
in
Mathematical Logic
by
JAYKISHAN
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103
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72
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probability
acebooklet
0
votes
1
answer
32
Proposition Logic Question
Are these propositions? 1.This sentence is true 2.This sentence is false Aren’t these liar paradox?
answered
May 30
in
Mathematical Logic
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ankitgupta.1729
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33
Kenneth Rosen Edition 7th Exercise 1.2 Question 34 (Page No. 24)
Five friends have access to a chat room. Is it possible to determine who is chatting if the following information is known? Either Kevin or Heather, or both, are chatting. Either Randy or Vijay, but not both, are ... either both chatting or neither is. If Heather is chatting, then so are Abby and Kevin. Explain your reasoning.
answered
May 29
in
Mathematical Logic
by
ankitgupta.1729
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34
Kenneth Rosen Edition 7th Exercise 1.2 Question 33 (Page No. 24)
Steve would like to determine the relative salaries of three coworkers using two facts. First, he knows that if Fred is not the highest paid of the three, then Janice is. Second, he knows that if Janice is not the lowest paid, ... and Janice from what Steve knows? If so, who is paid the most and who the least? Explain your reasoning.
answered
May 29
in
Mathematical Logic
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ankitgupta.1729
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35
Kenneth Rosen Edition 7th Exercise 1.2 Question 32 (Page No. 23)
The police have three suspects for the murder of Mr. Cooper: Mr. Smith, Mr Jones, Mr. Williams. Smith Jones, and Williams each declare that they did not kill Cooper. Smith also states that Cooper was friend of Jones and that ... telling the truth, but the statements of the guilty man may or may not b true? innocent men do not lie?
answered
May 29
in
Mathematical Logic
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ankitgupta.1729
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36
Kenneth Rosen Edition 7th Exercise 1.2 Question 23 (Page No. 23)
Relate to inhabitants of the island of knights and knaves created by Smullyan, where knights always tell the truth and knaves always lie. You encounter two people, $A$ and $B$. Determine, if possible, what $A$ and $B$ are if ... what these people are, can you draw any conclusions? $A$ says We are both knaves and $B$ says nothing.
answered
May 28
in
Mathematical Logic
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ankitgupta.1729
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kennethrosen
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37
Kenneth Rosen Edition 7th Exercise 1.2 Question 22 (Page No. 23)
Relate to inhabitants of the island of knights and knaves created by Smullyan, where knights always tell the truth and knaves always lie. You encounter two people, $A$ and $B$. Determine, if possible, what $A$ and $B$ are if they ... determine what these people are, can you draw any conclusions ? Both $A$ and $B$ say I am a knight.
answered
May 28
in
Mathematical Logic
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ankitgupta.1729
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38
Kenneth Rosen Edition 7th Exercise 1.2 Question 20 (Page No. 23)
relate to inhabitants of the island of knights and knaves created by Smullyan, where knights always tell the truth always lie. You encounter two people. A and B. Determine, if possible, what A and B are if they address you in the ways ... can you draw any conclusions? A says The two of us are both knights and B says A is knave.
answered
May 28
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Mathematical Logic
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ankitgupta.1729
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39
Kenneth Rosen Edition 7th Exercise 1.2 Question 19 (Page No. 23)
Relate to inhabitants of the island of knights and knaves created by Smullyan, where knights always tell the truth and knaves always lie. You encounter two people, $A$ and $B$. Determine, if possible, what $A$ and $B$ are if they address ... can you draw any conclusions ? $A$ says At least one of us is a knave and $B$ says nothing.
answered
May 28
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Mathematical Logic
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40
Kenneth Rosen Edition 7th Exercise 1.2 Question 17 (Page No. 23)
When three professors are seated in a restaurant, the hostess asks them: Does everyone want coffee ? The first professor says: I do not know. The second professor then says: I do not know. Finally, the third ... The hostess comes back and gives coffee to the professors who want it. How did she figure out who wanted coffee?
answered
May 28
in
Mathematical Logic
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ankitgupta.1729
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