Recent questions and answers in Mathematical Logic - GATE Overflow

+6 votes

6 answers

1

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 5 days ago in Mathematical Logic by habedo007 Active (2.4k points) | 5k views

+32 votes

7 answers

2

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 6 days ago in Mathematical Logic by Navneet Singh Tomar Junior (595 points) | 4.3k views

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 Active (4.4k points) | 394 views

+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

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 in Mathematical Logic by vupadhayayx86 Active (1.5k points) | 600 views

+23 votes

5 answers

6

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 in Mathematical Logic by manikantsharma (411 points) | 1.8k views

0 votes

0 answers

7

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 in Mathematical Logic by gatecse Boss (16.6k points) | 14 views

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

+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

+1 vote

2 answers

10

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 in Mathematical Logic by GoalSet1 (191 points) | 564 views

+2 votes

2 answers

11

Find the number of into functions

answered Aug 26 in Mathematical Logic by Lakshman Patel RJIT Veteran (53.4k points) | 1.3k views

+1 vote

1 answer

12

Knights , Knaves , spy

answered Aug 24 in Mathematical Logic by Kushagra गुप्ता Active (1.1k points) | 99 views

+27 votes

3 answers

13

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 in Mathematical Logic by sohailkhan (67 points) | 2.5k views

0 votes

1 answer

14

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 in Mathematical Logic by Rohit Suryanarayan (15 points) | 465 views

+55 votes

4 answers

15

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 in Mathematical Logic by MRINMOY_HALDER Active (2.9k points) | 4.3k views

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

+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

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 in Mathematical Logic by Lakshmikanta (55 points) | 155 views

+4 votes

2 answers

19

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 in Mathematical Logic by Satbir Boss (20.7k points) | 229 views

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

+4 votes

1 answer

21

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 in Mathematical Logic by Arjun Veteran (423k points) | 202 views

0 votes

1 answer

22

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 in Mathematical Logic by Arjun Veteran (423k points) | 168 views

+1 vote

2 answers

23

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 in Mathematical Logic by Satbir Boss (20.7k points) | 1.5k views

+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 (20.7k points) | 154 views

+26 votes

2 answers

25

GATE2005-41
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 Active (2.9k points) | 2.9k views

+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 Active (3.5k points) | 60 views

+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 (20.7k points) | 82 views

+15 votes

4 answers

28

TIFR2011-A-1
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 Veteran (117k points) | 724 views

+9 votes

4 answers

29

TIFR2010-A-4
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 by srestha Veteran (117k points) | 514 views

0 votes

1 answer

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 Veteran (117k points) | 40 views

+1 vote

0 answers

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 (103 points) | 72 views

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 by ankitgupta.1729 Boss (15.9k points) | 138 views

0 votes

1 answer

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 Boss (15.9k points) | 48 views

0 votes

2 answers

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 by ankitgupta.1729 Boss (15.9k points) | 34 views

0 votes

1 answer

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 by ankitgupta.1729 Boss (15.9k points) | 32 views

0 votes

1 answer

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 by ankitgupta.1729 Boss (15.9k points) | 26 views

0 votes

1 answer

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 by ankitgupta.1729 Boss (15.9k points) | 18 views

0 votes

1 answer

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 in Mathematical Logic by ankitgupta.1729 Boss (15.9k points) | 54 views

0 votes

1 answer

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 in Mathematical Logic by ankitgupta.1729 Boss (15.9k points) | 36 views

0 votes

1 answer

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 by ankitgupta.1729 Boss (15.9k points) | 33 views

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