Recent questions tagged mathematical-logic

0 votes

0 answers

1

Kenneth Rosen Nested Quantifiers Self Doubt
Q) There is somebody whom no one loves L(x,y) : x loves y. Doubt:- Does ∀x ∃y ~L(x,y) will be same as ∃x ∀y ~L(y,x) or both are different please give explaination

asked 6 days ago in Mathematical Logic by kd..... Junior (681 points) | 21 views

+1 vote

1 answer

2

Propositional logic self doubt
q = you can access the library r = you have a valid ID s = you have paid subscription fee of that day Consider the following English sentence “You cannot access the library if you don’t have a valid ID unless you have paid subscription fee of that day” which of the following is the correct logical expression? $q \rightarrow (r \vee s )$ $(q \rightarrow r) \vee s$

asked Jan 7 in Mathematical Logic by Mk Utkarsh Boss (32.9k points) | 35 views

0 votes

0 answers

3

In Mathematical Logic formula and well formed formula are same?
https://stackoverflow.com/questions/35835333/formula-vs-well-formed-formula-in-propositional-logic ← Here the commenter wrote there is almost no situation in logic when "formula" does not mean "well-formed formula Q1 :- ... Automata Theory (Which I haven't completed)) Q3 :- Is Formula and Well formed Formula are same?

asked Dec 26, 2018 in Mathematical Logic by newbie (59 points) | 30 views

0 votes

0 answers

4

Quantifiers
Translate into the predicate logic One has to drink water in order to survive D(x) = x drinks water S(x) = x survives

asked Dec 9, 2018 in Mathematical Logic by kd..... Junior (681 points) | 39 views

0 votes

0 answers

5

Propositional Logic
Which of the following is the best English translation for All humans eat alligator Alligator eats only human Every Alligator Eats Human Only Alligator eats Human

asked Dec 8, 2018 in Mathematical Logic by Na462 Loyal (8k points) | 50 views

+1 vote

0 answers

6

TIFR 2017
The notation ⇒ denotes implies and ∧ denotes and in the following formulae. Let X denote the formula: (b ⇒ a) ⇒ (a ⇒ b) Let Y denote the formula: (a ⇒ b) ∧ b Which of the following is TRUE? (a) X is satisfiable and Y is not satisfiable. (b) X ... is not a tautology and Y is not satisfiable. (d) X is not a tautology and Y is satisfiable. (e) X is a tautology and Y is satisfiable.

asked Dec 6, 2018 in Mathematical Logic by suparna kar (125 points) | 65 views

0 votes

0 answers

7

Tautology
Consider the following statements: $P_1$: Sachin Tendulkar gets out before the tea break only if Ishant Sharma comes out to bat. $P_2$: Ishant Sharma won't come out to bat, if Lasith Malinga is not called to bowl. $P_3$: Sachin Tendulkar got out before the tea break. Which ... Keeping A, B, C option as X one by one, and all follows, thus option D is correct but given answer is C.

asked Nov 29, 2018 in Mathematical Logic by Shubhanshu Boss (17.8k points) | 29 views

0 votes

1 answer

8

why is the conclusion incorrect for the below premises ?
I am getting the conclusion to be true by Proof by Contradiction , what's wrong in the approach ?

asked Nov 13, 2018 in Mathematical Logic by radha gogia Loyal (8k points) | 102 views

+2 votes

1 answer

9

GATEBOOK-2019-DM1-1
Which of the following first order logic statement is equivalent to below statement? If anyone cheats, everyone suffers. $S_1 \forall x (\text{cheat}(x) \to \forall y \text{ suffer}(y))$ $S_2: \forall x\forall y (\text{cheat}(x) \to \text{ suffer}(y))$ Only $S1$ Only $S2$ Both $S1$ and $S2$ None

asked Oct 28, 2018 in Mathematical Logic by GATEBOOK Boss (12.6k points) | 213 views

0 votes

1 answer

10

GATEBOOK-2019-DM1-2
Which of the following first order logic statements is VALID? $\neg\forall x \{ P(x) \vee ∃y [Q(y) \wedge P(y)] \} ≡ ∃x \{ \neg P(x) \wedge \forall y [(P(y) → \neg Q(y)) \vee (Q(y) → \neg P(y))] \}$ ...

asked Oct 28, 2018 in Mathematical Logic by GATEBOOK Boss (12.6k points) | 103 views

0 votes

1 answer

11

GATEBOOK-2019-DM1-3
Which of the following formulae is a formalization of the sentence: "There is a $\text{Computer}$ which is not used by any $\text{Student}$" $ \exists x (\text{Computer}(x) \wedge \forall y. (\sim \text{Student}(y) \wedge \sim \text{Uses}(y,x))) $ ... $ \exists x (\text{Computer} (x) \rightarrow \forall y . (\sim \text{Student} (y) \wedge \sim \text{Uses}(y,x)))$

asked Oct 28, 2018 in Mathematical Logic by GATEBOOK Boss (12.6k points) | 71 views

0 votes

1 answer

12

GATEBOOK-2019-DM1-4
Minesweeper is a single-player computer game invented by Robert Donner in 1989. A unary predicate mine is defined, where $\text{mine}(x)$ means that the cell $x$ ... $n$ mines in the game There are at most $n$ mines in the game None of the above

asked Oct 28, 2018 in Mathematical Logic by GATEBOOK Boss (12.6k points) | 186 views

0 votes

0 answers

13

GATEBOOK-2019-DM1-5
Which of the below first order logic formulae represent the sentence There is a student who is loved by every other student Here, $\text{Loves}(x,y)$ means $x$ loves $y$ ...

asked Oct 28, 2018 in Mathematical Logic by GATEBOOK Boss (12.6k points) | 89 views

0 votes

0 answers

14

GATEBOOK-2019-DM1-6
Which of the following propositional formulae represents the sentence, 'He will come in the $8:15$ or the $9:15$ train; if the former, he will have time to visit us', where $p$ means 'He will come in the $8:15$ train' $q$ means 'He will come in the $9:15$ train' $r$ ... $ ( p \rightarrow q) \wedge ( p \vee r )$ $ (p \vee q ) \wedge (p \rightarrow r)$

asked Oct 28, 2018 in Mathematical Logic by GATEBOOK Boss (12.6k points) | 88 views

+2 votes

1 answer

15

GATEBOOK-2019-DM1-7
Which of the following propositional formulae is a tautology? $(\neg p \vee r ) \rightarrow (p \vee \neg r)$ $ \neg ( p \rightarrow (p \wedge q ))$ $ r \rightarrow ( p \wedge \neg r )$ $ ( p \leftrightarrow q ) \vee (p \leftrightarrow \neg q)$

asked Oct 28, 2018 in Mathematical Logic by GATEBOOK Boss (12.6k points) | 62 views

0 votes

1 answer

16

GATEBOOK-2019-DM1-8
Which of the following inference system is valid? $ (p \vee q ) \rightarrow r, r \models \neg p $ $ p, \neg p \leftrightarrow q \models \neg q$ $ (p \wedge q) \rightarrow r, \neg r \models p \vee q$ $ p \wedge q \models p \leftrightarrow \neg q$

asked Oct 28, 2018 in Mathematical Logic by GATEBOOK Boss (12.6k points) | 67 views

+1 vote

0 answers

17

GATEBOOK-2019-DM1-9
Which of the following formulas represents the sentence, 'Share prices will go up, and if interest rates go up too, there will be a recession', where ; $p$ means 'share prices will go up' $q$ means 'interest rates will go up' $r$ means 'there will be a recession'. $ p \wedge q \rightarrow r$ $ p \wedge (q \rightarrow r)$ $ p \rightarrow q \wedge r$ $ (p \rightarrow q) \vee r$

asked Oct 28, 2018 in Mathematical Logic by GATEBOOK Boss (12.6k points) | 117 views

+2 votes

1 answer

18

GATEBOOK-2019-DM1-10
Assuming a non-empty universe, the formula $(\forall x P(x) \vee \exists y P(y))$ is equivalent to $\exists x (P(x))$ $ (\forall x P(x))$ $ \neg (\forall x P(x))$ $ \neg (\exists x (P(x))$

asked Oct 28, 2018 in Mathematical Logic by GATEBOOK Boss (12.6k points) | 115 views

0 votes

0 answers

19

GATEBOOK-2019-DM1-11
Suppose that $P(x,y)$ means "x is a parent of y" and $M(x)$ means "x is a male". If $F(v,w)$ equals $M(v) \wedge \exists x \exists y (P(x,y) \wedge P(x,v) \wedge (y \neq v ) \wedge P(y,w)), $ the meaning of the expression $F(v,w)$ is $v$ is a brother of $w$ $v$ is an uncle of $w$ $v$ is a grandfather of $w$ $v$ is a nephew of $w$

asked Oct 28, 2018 in Mathematical Logic by GATEBOOK Boss (12.6k points) | 54 views

0 votes

1 answer

20

GATEBOOK-2019-DM1-12
Translate the following logic statement to English where, $A(x)$: $x$ is African, $F(x,y)$: x and y are friends. The universe for $x$ and $y$ is all the people in the world. $\forall x \exists y((A(x) \vee (F(x,y)))$ Every African has some African friend Every person who is not African has at least one friend Every person who has friend is not African None of these

asked Oct 28, 2018 in Mathematical Logic by GATEBOOK Boss (12.6k points) | 130 views

+1 vote

1 answer

21

GATEBOOK-2019-DM1-13
Consider the following statement $ \exists x \: \exists y (\text{PARENT}(x, \text{Ramu}) \wedge \text{PARENT}(y, \text{Ramu}))$ where $\text{PARENT}(x,y)$ means $x$ is a parent of $y.$ Which of the following statement is true about ... order logic statement ? Ramu has at least one parent Ramu has at least two parents Ramu has at most one parent Ramu has at most two parents

asked Oct 28, 2018 in Mathematical Logic by GATEBOOK Boss (12.6k points) | 107 views

+1 vote

0 answers

22

GATEBOOK-2019-DM1-14
Consider the following inference system: $P$ $\neg P \vee Q$ $\neg Q \vee R$ Which of the following is a valid conclusion ? $R$ $ \neg R$ $ \neg Q$ $ \neg R \wedge Q$

asked Oct 28, 2018 in Mathematical Logic by GATEBOOK Boss (12.6k points) | 61 views

+2 votes

1 answer

23

GATEBOOK-2019-DM1-15
Let $I$ denote the formula $ (q \rightarrow p) \rightarrow (p \rightarrow q)$ and $II$ denote the formula $(p\rightarrow q) \wedge q$ Which of the following is true? $I$ is not tautology and $II$ is not satisfiable $I$ is not tautology and $II$ is satisfiable $I$ is satisfiable and $II$ is not satisfiable $I$ is tautology and $II$ is satisfiable

asked Oct 28, 2018 in Mathematical Logic by GATEBOOK Boss (12.6k points) | 86 views

+1 vote

0 answers

24

GATEBOOK-2019-DM1-16
Which of the following statements is not necessarily true ? $\forall x \: \forall y P(x,y) \Leftrightarrow \forall y \: \forall x P(x,y)$ $ \exists x \: \exists y P(x,y) \Leftrightarrow \exists y \: \exists x P(x,y)$ $\forall x \: \exists y P(x,y) \Rightarrow \exists y \: \forall x P(x,y) $ $ \exists y \:\forall x P(x,y) \Rightarrow \forall x \: \exists y P(x,y)$

asked Oct 28, 2018 in Mathematical Logic by GATEBOOK Boss (12.6k points) | 64 views

0 votes

1 answer

25

GATEBOOK-2019-DM1-17
Every true Indian thinks about politics and Jayaprakash Narayana thinks about politics Which of the following is valid conclusion? Jayaprakash Narayana is true Indian Jayaprakash Narayana is politician Jayaprakash Narayana is not true Indian None of the above

asked Oct 28, 2018 in Mathematical Logic by GATEBOOK Boss (12.6k points) | 62 views

+2 votes

1 answer

26

GATEBOOK-2019-DM1-18
Everyone has exactly one best friend Which of the following first order logic statements correctly represents above English statement? $BF(x,y)$ means $x$ and $y$ are best friends $S1 : \forall x \exists y \forall z (BF(x,y) \wedge \sim BF(x,z) \rightarrow (y \neq z))$ ... $S1$ Only $S2$ Both $S1$ and $S2$ None of the two

asked Oct 28, 2018 in Mathematical Logic by GATEBOOK Boss (12.6k points) | 117 views

+2 votes

1 answer

27

GATEBOOK-2019-DM1-19
Which of the following statements is FALSE $\exists x (P(x) \rightarrow Q(x)) \equiv \forall x P(x) \rightarrow \exists x Q(x) $ $\exists x (P(x) \vee Q(x)) \equiv \exists x P(x) \vee \exists x Q(x) $ $\forall x (P(x)\wedge Q(x)) \equiv \forall x P(x) \wedge \forall x Q(x) $ $\exists x (P(x)\wedge Q(x)) \equiv \exists x P(x) \wedge \exists x Q(x) $

asked Oct 28, 2018 in Mathematical Logic by GATEBOOK Boss (12.6k points) | 76 views

0 votes

1 answer

28

GATEBOOK-2019-DM1-20
A binary operator is defined as follows $P \Updownarrow Q = \sim P \wedge Q$ Which of the following statement is equivalent to $P \rightarrow Q $ $\sim P \Updownarrow Q$ $\sim( P \Updownarrow Q)$ $\sim( \sim P \Updownarrow Q)$ $\sim ( \sim P \Updownarrow \sim Q)$

asked Oct 28, 2018 in Mathematical Logic by GATEBOOK Boss (12.6k points) | 36 views

0 votes

0 answers

29

Quantifiers
Given that B(x) means "x is a bear" F(x) means "x is a fish" and E(x,y) means "x eats y" What is the best English translation of $\forall x [F(x)\rightarrow \forall y(E(y,x)\rightarrow B(y))]$ A) All fish eat bears B) Every bears can eat fish C) Only bears eat fish D) Bears eat only fish

asked Oct 2, 2018 in Mathematical Logic by Lakshman Patel RJIT Boss (26.4k points) | 51 views

0 votes

0 answers

30

Nested Quantifiers
If we have ∀x(p(x)) then in boolean algebra form we can write this statement as (P1 + P2) where + signifies OR which makes it very easy to deal with. So likewise is there any way to have a view of a statement like ∀x∀y(R(x,y)) into boolean form?

asked Sep 29, 2018 in Mathematical Logic by sushil1997 (25 points) | 35 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 tagged mathematical-logic

Recent Posts

Recent Blog Comments