Recent questions and answers in Mathematical Logic - GATE Overflow

0 votes

1 answer

1

Maths
HOW MANY ways we can distribute 10 objects to 3 children so that every child gets atleast one object?

answered 3 days ago in Mathematical Logic by Raghav Khajuria Junior (807 points) | 58 views

+33 votes

5 answers

2

GATE2011-30
Which one of the following options is CORRECT given three positive integers $x, y$ and $z$ ... is always true irrespective of the value of $x$ $P(x)$ being true means that $x$ has exactly two factors other than $1$ and $x$

answered 4 days ago in Mathematical Logic by Rishiryanemo (29 points) | 3.9k views

+31 votes

8 answers

3

GATE2005-IT-36
Let $P(x)$ and $Q(x)$ ...

answered Jan 16 in Mathematical Logic by Madhab Loyal (5.8k points) | 4.6k views

0 votes

1 answer

4

ugc net 2018 july-79

answered Jan 14 in Mathematical Logic by mishrapankajs (11 points) | 250 views

+2 votes

1 answer

5

ISRO2020-73
Given that $B(a)$ means “$a$ is a bear” $F(a)$ means “$a$ is a fish” and $E(a,b)$ means “$a $ eats $b$” Then what is the best meaning of $\forall x [F(x) \to \forall y(E(y,x)\rightarrow b(y))]$ Every fish is eaten by some bear Bears eat only fish Every bear eats fish Only bears eat fish

answered Jan 13 in Mathematical Logic by chirudeepnamini Active (4.5k points) | 245 views

0 votes

1 answer

6

Kenneth Rosen Edition 7th Exercise 1.7 Question 7 (Page No. 91)
Use a direct proof to show that every odd integer is the difference of two squares.

answered Jan 5 in Mathematical Logic by vedantbonde19 (29 points) | 23 views

0 votes

1 answer

7

Kenneth Rosen Edition 7th Exercise 1.7 Question 15 (Page No. 91)
Use a proof by contraposition to show that if $x+y≥2$,where $x$ and $y$ are real numbers, then $x≥1$ or $y≥1$.

answered Jan 5 in Mathematical Logic by vedantbonde19 (29 points) | 13 views

+1 vote

1 answer

8

Kenneth Rosen Edition 7th Exercise 1.7 Question 11 (Page No. 91)
Prove or disprove that the product of two irrational numbers is irrational.

answered Jan 5 in Mathematical Logic by vedantbonde19 (29 points) | 22 views

+1 vote

1 answer

9

Kenneth Rosen Edition 7th Exercise 1.7 Question 10 (Page No. 91)
Use a direct proof to show that the product of two rational numbers is rational.

answered Jan 5 in Mathematical Logic by vedantbonde19 (29 points) | 9 views

+1 vote

1 answer

10

ME FLT
Consider the following statements with respect to POSETs. I. Every non empty, finite POSET has at least one maximal and at least one minimal element. II. Every POSET has at most one greatest element and at most one least element. Which of the above statement(s) is/are true?

answered Jan 1 in Mathematical Logic by Veenit Active (1.6k points) | 44 views

+24 votes

4 answers

11

GATE1998-1.5
What is the converse of the following assertion? I stay only if you go I stay if you go If I stay then you go If you do not go then I do not stay If I do not stay then you go

answered Dec 31, 2019 in Mathematical Logic by JashanArora Loyal (6.9k points) | 3.5k views

0 votes

3 answers

12

Express the statement in logical expression
Express the statement "Everyone has exactly one best friend" as a logical expression involving predicates,quantifiers with a domain consisting of all people,and logical connectives without using uniqueness quantifier. I am confused pleased explain it

answered Dec 28, 2019 in Mathematical Logic by rohithk (11 points) | 473 views

0 votes

2 answers

13

GATE Minimum Spanning Trees
Q1) Why is the path between a pair of vertices in a minimum Spanning tree of an undirected graph not the shortest( minimum weight) path?

answered Dec 17, 2019 in Mathematical Logic by smsubham Boss (11.8k points) | 190 views

+2 votes

1 answer

14

Hamiltonian Graph
A complement of a cyclic graph on 5 vertices , has an Hamiltonian circuit . (True/False)

answered Dec 11, 2019 in Mathematical Logic by Anup dogrial (339 points) | 284 views

+26 votes

3 answers

15

GATE1991-15,b
Consider the following first order formula: ... Does it have finite models? Is it satisfiable? If so, give a countable model for it.

answered Dec 11, 2019 in Mathematical Logic by pritishc Active (2.2k points) | 1.9k views

+13 votes

8 answers

16

GATE2019-35
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 Dec 10, 2019 in Mathematical Logic by Deepakk Poonia (Dee) Boss (27.6k points) | 6k views

+37 votes

7 answers

17

GATE2008-IT-21
Which of the following first order formulae is logically valid? Here $\alpha(x)$ is a first order formula with $x$ as a free variable, and $\beta$ ... $[(\forall x, \alpha(x)) \rightarrow \beta] \rightarrow [\forall x, \alpha(x) \rightarrow \beta]$

answered Nov 26, 2019 in Mathematical Logic by JashanArora Loyal (6.9k points) | 4.7k views

+33 votes

7 answers

18

GATE2002-1.8
"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 Nov 11, 2019 in Mathematical Logic by Navneet Singh Tomar Junior (783 points) | 4.8k views

0 votes

2 answers

19

solution of rosen
can anyone has the soft copy of kenneth h rosen solutions?

answered Nov 11, 2019 in Mathematical Logic by Ram Swaroop Loyal (5.4k points) | 439 views

+2 votes

3 answers

20

Rosen chapter 5.5 question 50
How many ways are there to distribute 5 distinguishable objects into three indistinguishable boxes?

answered Nov 9, 2019 in Mathematical Logic by SaurabhKatkar (241 points) | 245 views

+10 votes

4 answers

21

GATE1989-3-v
Answer the following: Which of the following well-formed formulas are equivalent? $P \rightarrow Q$ $\neg Q \rightarrow \neg P$ $\neg P \vee Q$ $\neg Q \rightarrow P$

answered Oct 8, 2019 in Mathematical Logic by vupadhayayx86 Active (1.7k points) | 676 views

+25 votes

5 answers

22

GATE2009-23
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, 2019 in Mathematical Logic by manikantsharma (429 points) | 2k views

0 votes

0 answers

23

CMI2019-B-5
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, 2019 in Mathematical Logic by gatecse Boss (17.5k points) | 52 views

0 votes

1 answer

24

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, 2019 in Mathematical Logic by tejamach (11 points) | 25 views

+1 vote

1 answer

25

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, 2019 in Mathematical Logic by Akashniranjan (17 points) | 670 views

+1 vote

2 answers

26

UGCNET-June2013-II-40
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, 2019 in Mathematical Logic by GoalSet1 (215 points) | 589 views

+2 votes

2 answers

27

Find the number of into functions

answered Aug 26, 2019 in Mathematical Logic by Lakshman Patel RJIT Veteran (59.3k points) | 1.4k views

+1 vote

1 answer

28

Knights , Knaves , spy

answered Aug 24, 2019 in Mathematical Logic by Kushagra गुप्ता Active (4.5k points) | 104 views

+30 votes

3 answers

29

GATE2014-3-1
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, 2019 in Mathematical Logic by sohailkhan (75 points) | 2.9k views

0 votes

1 answer

30

recurrence relation
Which recurrence relation satisfy the sequence: 2, 3, 4, . . ., for n ≥ 1. A ) T(N) = 2 T(N-1) - T(N-2) B)T(N) = T(N-1) + T(N-2) C)T(N) = N+1 D) None of these

answered Aug 8, 2019 in Mathematical Logic by Rohit Suryanarayan (17 points) | 530 views

+58 votes

4 answers

31

GATE2003-33
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, 2019 in Mathematical Logic by MRINMOY_HALDER Active (4k points) | 4.8k views

0 votes

1 answer

32

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, 2019 in Mathematical Logic by bankeshk (79 points) | 64 views

+1 vote

1 answer

33

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, 2019 in Mathematical Logic by mohan123 Active (1.7k points) | 83 views

+5 votes

2 answers

34

UGCNET-June-2019-II-8
Match List-I with List-II: ... ) - (iv); (b) - (i); (c) - (iii); (d) - (ii) (a) - (iv); (b) - (iii); (c) - (i); (d) - (ii)

answered Jul 7, 2019 in Mathematical Logic by Lakshmikanta (69 points) | 218 views

+4 votes

2 answers

35

UGCNET-June-2019-II-6
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, 2019 in Mathematical Logic by Satbir Boss (24.2k points) | 337 views

0 votes

1 answer

36

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, 2019 in Mathematical Logic by vizzard110 (439 points) | 51 views

+4 votes

1 answer

37

TIFR2017-B-6
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, 2019 in Mathematical Logic by Arjun Veteran (431k points) | 249 views

0 votes

1 answer

38

GATE1988-14i
Consider the following well-formed formula: $\exists x \forall y [ \neg \: \exists z [ p (y, z) \wedge p (z, y) ] \equiv p(x,y)]$ Express the above well-formed formula in clausal form.

answered Jun 7, 2019 in Mathematical Logic by Arjun Veteran (431k points) | 183 views

+1 vote

2 answers

39

UGCNET-Dec2015-II-6
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, 2019 in Mathematical Logic by Satbir Boss (24.2k points) | 1.5k views

+3 votes

1 answer

40

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?

asked Jun 4, 2019 in Mathematical Logic by srestha Veteran (119k points) | 196 views

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