Recent questions and answers in Mathematical Logic

+1 vote

1 answer

1

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 5 days ago in Mathematical Logic by mohan123 (215 points) | 60 views

0 votes

2 answers

2

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

answered Jul 7 in Mathematical Logic by Lakshmikanta (27 points) | 50 views

0 votes

2 answers

3

UGCNET-June-2019-II-6
Which of the following is principal conjunctive normal form for $[(p\vee q)\wedge\ \neg p \rightarrow \neg q ]$ ? $p\vee \neg q$ $p \vee q $ $\neg p \vee q$ $\neg p \vee \neg\ q$

answered Jul 7 in Mathematical Logic by Satbir Boss (15.3k points) | 56 views

0 votes

1 answer

4

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 (85 points) | 30 views

+3 votes

1 answer

5

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 (413k points) | 182 views

0 votes

1 answer

6

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 (413k points) | 149 views

+1 vote

2 answers

7

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 (15.3k points) | 1.4k views

0 votes

1 answer

8

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 (15.3k points) | 97 views

+25 votes

2 answers

9

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 (1.3k points) | 2.7k views

0 votes

1 answer

10

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 (3.3k points) | 39 views

+1 vote

1 answer

11

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 (15.3k points) | 71 views

+13 votes

4 answers

12

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 (112k points) | 655 views

+7 votes

4 answers

13

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 (112k points) | 471 views

0 votes

1 answer

14

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 (112k points) | 30 views

0 votes

0 answers

15

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 (83 points) | 60 views

0 votes

1 answer

16

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 (13.7k points) | 104 views

0 votes

1 answer

17

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 (13.7k points) | 38 views

0 votes

2 answers

18

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 (13.7k points) | 29 views

0 votes

1 answer

19

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 (13.7k points) | 27 views

0 votes

1 answer

20

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 (13.7k points) | 25 views

0 votes

1 answer

21

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 (13.7k points) | 16 views

0 votes

1 answer

22

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 (13.7k points) | 50 views

0 votes

1 answer

23

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 (13.7k points) | 31 views

0 votes

1 answer

24

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 (13.7k points) | 23 views

0 votes

0 answers

25

Self Doubt-LA
In a non-homogeneous equation Ax = b, x has a unique solution when $A^{-1}$ exists i.e x = $A^{-1}$b but when det(A) = 0 then we have infinite solution or many solution. please give a mathematical explanation of how the 2nd statement occurs?

asked May 26 in Mathematical Logic by MRINMOY_HALDER Active (1.3k points) | 32 views

+1 vote

0 answers

26

Self Doubt:Mathematical Logic
Represent these two statement in first order logic: $A)$ Only Alligators eat humans $B)$ Every Alligator eats humans Is Every represents $\equiv \exists$ and Only represents $\equiv \forall$ ?? Can we differentiate it with verb ‘eat’ and ‘eats’??

asked May 18 in Mathematical Logic by srestha Veteran (112k points) | 40 views

0 votes

0 answers

27

self doubt consistency and satisfiability
how can we link consistency and satisfiability ? are they bidirectional? plz help

asked May 10 in Mathematical Logic by Manoj Kumar Pandey (153 points) | 20 views

0 votes

0 answers

28

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.

asked May 1 in Mathematical Logic by souren (37 points) | 45 views

0 votes

0 answers

29

Made Easy Test Series:Discrete Math-Mathematical 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

asked Apr 27 in Mathematical Logic by srestha Veteran (112k points) | 47 views

0 votes

1 answer

30

self doubt about maths practice
Where can i find only maths PYQ all branches . for practice ?

answered Apr 26 in Mathematical Logic by gaurav1.yuva (427 points) | 30 views

0 votes

0 answers

31

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 (41 points) | 41 views

0 votes

0 answers

32

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 by kaveeshnyk (37 points) | 27 views

0 votes

0 answers

33

linear programming

asked Apr 12 in Mathematical Logic by shruti gupta1 (407 points) | 21 views

0 votes

0 answers

34

Kenneth Rosen Edition 7th Exercise 2.3 Question 51 (Page No. 154)
Show that if $x$ is a real number and $n$ is an integer, then $x<n$ if and only if $\left \lfloor x \right \rfloor < n$ $n<x$ if and only if $ n<=\left \lfloor x \right \rfloor $

asked Apr 9 in Mathematical Logic by Pooja Khatri Boss (10.8k points) | 33 views

+1 vote

0 answers

35

Kenneth Rosen Edition 7th Exercise 2.3 Question 11 (Page No. 153)
Determine whether each of these functions form $[a,b,c,d]$ to itself is onto? $f(a)=b, f(b)=a,f(c)=c,f(d)=d$ $f(a)=b, f(b)=b,f(c)=d,f(d)=c$ $f(a)=d, f(b)=b,f(c)=c,f(d)=d$

asked Apr 9 in Mathematical Logic by Pooja Khatri Boss (10.8k points) | 22 views

0 votes

0 answers

36

Kenneth Rosen Edition 7th Exercise 2.1 Question 16 (Page No. 126)
Use a Venn diagram to illustrate the relationships $A \subset B$ and $ A \subset C.$

asked Apr 5 in Mathematical Logic by Pooja Khatri Boss (10.8k points) | 5 views

+1 vote

1 answer

37

Kenneth Rosen Edition 7th Exercise 2.1 Question 9 (Page No. 125)
Determine whether each of these statements is true or false. $0$ $ \epsilon$ $\phi$ $\phi$ $\epsilon$ {$0$} {$0$} $ \subset$ {$ \phi$} $\phi$ $\subset$ {$0$} {$0$} $\epsilon$ {$0$} {$0$} $\subset$ {$0$} {$\phi$} $\subseteq$ {$\phi$}

answered Apr 5 in Mathematical Logic by tusharp Loyal (6.6k points) | 38 views

0 votes

0 answers

38

DDA Direct Recruitment 2019 - Asst. System Director
Which of the following gives the predicate logic representation of the sentence Ram was a man ? Ram $\rightarrow$ man $\forall x:$ Ram (x) $\rightarrow$ man (x) Man (Ram) Man $\rightarrow$ Ram I have marked option ... I want to raise an objection to this answer. Kindly provide a reliable source which confirms the correct answer for this question.

asked Apr 5 in Mathematical Logic by zeeshanmohnavi Junior (837 points) | 73 views

0 votes

0 answers

39

Kenneth Rosen Edition 7th Exercise 1.7 Question 42 (Page No. 92)
Prove that these four statements about the integer $n$ are equivalent: $n^2$is odd, $1−n$ is even, $n^3$ is odd, $n^2+1$ is even.

asked Apr 4 in Mathematical Logic by Pooja Khatri Boss (10.8k points) | 25 views

0 votes

0 answers

40

Kenneth Rosen Edition 7th Exercise 1.7 Question 41 (Page No. 92)
Prove that if $n$ is an integer, these four statements are equivalent: $n$ is even, $n+1$ is odd, $3n+1$isodd, $3n$ is even.

asked Apr 4 in Mathematical Logic by Pooja Khatri Boss (10.8k points) | 11 views

tags	tag:apple
author	user:martin
title	title:apple
content	content:apple
exclude	-tag:apple
force match	+apple
views	views:100
score	score:10
answers	answers:2
is accepted	isaccepted:true
is closed	isclosed:true

Recent questions and answers in Mathematical Logic

Recent Posts

Recent Blog Comments