Recent questions tagged first-order-logic / GATE Overflow for GATE CSE

12 votes

2 answers

121

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 11
Translate the following sentences into First-order logic (FOL): If someone is noisy, everybody is annoyed. Use the following predicates : $\text{N}(x)\;:$ $x$ is noisy $\text{A}(x)\;:$ $x$ is annoyed Which of the ... $\forall x(\text{N}(x) \rightarrow \forall y(\text{A}(y)))$

Translate the following sentences into First-order logic (FOL): “ If someone is noisy, everybody is annoyed.”Use the following predicates :$\text{N}(x)\;:$ “$x$ is ...

GO Classes

644 views

GO Classes asked Apr 14, 2022

10 votes

2 answers

122

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 3
Which of the following is the negation of “there is a successful person who is grateful”? There is a successful person who is ungrateful. Every grateful person is unsuccessful. Every unsuccessful person is grateful. Every successful person is ungrateful.

Which of the following is the negation of “there is a successful person who is grateful”?There is a successful person who is ungrateful.Every grateful person is unsuc...

GO Classes

532 views

GO Classes asked Apr 14, 2022

8 votes

1 answer

123

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 13
Consider the following predicates. $\text{Rabbit}(x) = x$ is a rabbit. $\text{Cute}(x) = x$ is cute. Consider the following statement $\text{E},$ where the domain of every variable is set of all animals in a ... no cute rabbit in jungle $\text{J}.$ There is some rabbit who is not cute in jungle $\text{J}.$

Consider the following predicates.$\text{Rabbit}(x) = x$ is a rabbit.$\text{Cute}(x) = x$ is cute.Consider the following statement $\text{E},$ where the domain of every v...

GO Classes

442 views

GO Classes asked Apr 14, 2022

7 votes

2 answers

124

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 4
Consider the following predicates. $\text{Rabbit}(x) = x$ is a rabbit. $\text{Cute}(x) = x$ is cute. Consider the following statement $\text{E},$ ... $\text{J}.$

Consider the following predicates.$\text{Rabbit}(x) = x$ is a rabbit.$\text{Cute}(x) = x$ is cute.Consider the following statement $\text{E},$ where the domain of every v...

GO Classes

537 views

GO Classes asked Apr 14, 2022

3 votes

1 answer

125

GO Classes 2023 | Weekly Quiz 7 | Question: 1
Let $\text{M}(x)$ denote the predicate $x$ is a mobile ; $\text{B}(x)$ denote the predicate $x$ is black ; $\text{C}(x)$ denote the predicate $x$ has calculator . Suppose that the universe is set of all mobiles. Which of the following ... $: \forall x ( \text{M}(x) \wedge \text{C}(x) )$

Let$\text{M}(x)$ denote the predicate “$x$ is a mobile”;$\text{B}(x)$ denote the predicate “$x$ is black”;$\text{C}(x)$ denote the predicate “$x$ has calculator...

GO Classes

845 views

GO Classes asked Apr 14, 2022

1 votes

1 answer

126

GO Classes 2023 | Weekly Quiz 7 | Question: 2
Let the universe be the set of all integers. Which of the following statements is/are true? (Where “$+$” is the integer addition) $\forall x \forall y \exists z (x+y = z)$ $\forall x \exists y \forall z (x+y = z)$ $\exists x \forall y \exists z (x+y = z)$ $\exists z \forall x \exists y (x+y = z)$

Let the universe be the set of all integers. Which of the following statements is/are true? (Where “$+$” is the integer addition)$\forall x \forall y \exists z (x+y =...

GO Classes

347 views

GO Classes asked Apr 14, 2022

3 votes

2 answers

127

GO Classes 2023 | Weekly Quiz 7 | Question: 4
Consider the following statement $\text{S}$ in an universe $\text{U}.$ $\text{S} : \forall x \forall y (x = y)$ What is the maximum cardinality of $\text{U}$ such that $\text{S}$ is true?

Consider the following statement $\text{S}$ in an universe $\text{U}.$$\text{S} : \forall x \forall y (x = y)$What is the maximum cardinality of $\text{U}$ such that $\te...

GO Classes

380 views

GO Classes asked Apr 14, 2022

1 votes

1 answer

128

GO Classes 2023 | Weekly Quiz 7 | Question: 8
Consider the formula $\exists x \exists y \exists z(\text{R}(x, y) \wedge \text{R}(z, y) \wedge \text{R}(x, z) \wedge \neg \text{R}(z, x)).$ For which of the following interpretations, is this formula true? $(\text{N}$ ... $\text{R}(x,y) : y = x0 \;\text{or}\; y = x1.$

Consider the formula $\exists x \exists y \exists z(\text{R}(x, y) \wedge \text{R}(z, y) \wedge \text{R}(x, z) \wedge \neg \text{R}(z, x)).$For which of the following int...

GO Classes

374 views

GO Classes asked Apr 14, 2022

2 votes

1 answer

129

UGC NET CSE | October 2020 | Part 2 | Question: 40
Consider the following argument with premise $\forall _x (P(x) \vee Q(x))$ and conclusion $(\forall _x P(x)) \wedge (\forall _x Q(x))$ ... $(E)$ are not correct inferences Steps $(D)$ and $(F)$ are not correct inferences Step $(G)$ is not a correct inference

Consider the following argument with premise $\forall _x (P(x) \vee Q(x))$ and conclusion $(\forall _x P(x)) \wedge (\forall _x Q(x))$$\begin{array}{|ll|l|} \hline (A) & ...

go_editor

988 views

go_editor asked Nov 20, 2020

0 votes

3 answers

130

NIELIT 2017 DEC Scientist B - Section B: 43
Which one is the correct translation of the following statement into mathematical logic? “None of my friends are perfect.” $\neg\:\exists\:x(p(x)\land q(x))$ $\exists\:x(\neg\:p(x)\land q(x))$ $\exists\:x(\neg\:p(x)\land\neg\:q(x))$ $\exists\:x(p(x)\land\neg\:q(x))$

Which one is the correct translation of the following statement into mathematical logic?“None of my friends are perfect.”$\neg\:\exists\:x(p(x)\land q(x))$$\exists\:x...

admin

1.3k views

admin asked Mar 30, 2020

2 votes

6 answers

131

UGC NET CSE | January 2017 | Part 3 | Question: 60
The first order logic (FOL) statement $((R\vee Q)\wedge(P\vee \neg Q))$ is equivalent to which of the following? $((R\vee \neg Q)\wedge(P\vee \neg Q)\wedge (R\vee P))$ $((R\vee Q)\wedge(P\vee \neg Q)\wedge (R\vee P))$ $((R\vee Q)\wedge(P\vee \neg Q)\wedge(R\vee \neg P))$ $((R\vee Q)\wedge(P\vee \neg Q)\wedge (\neg R\vee P))$

The first order logic (FOL) statement $((R\vee Q)\wedge(P\vee \neg Q))$ is equivalent to which of the following?$((R\vee \neg Q)\wedge(P\vee \neg Q)\wedge (R\vee P))$$((R...

go_editor

2.9k views

go_editor asked Mar 24, 2020

42 votes

9 answers

132

GATE CSE 2020 | Question: 39
Which one of the following predicate formulae is NOT logically valid? Note that $W$ is a predicate formula without any free occurrence of $x$. $\forall x (p(x) \vee W) \equiv \forall x \: ( px) \vee W$ ... $\exists x(p(x) \rightarrow W) \equiv \forall x \: p(x) \rightarrow W$

Which one of the following predicate formulae is NOT logically valid?Note that $W$ is a predicate formula without any free occurrence of $x$.$\forall x (p(x) \vee W) \equ...

Arjun

17.3k views

Arjun asked Feb 12, 2020

7 votes

3 answers

133

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

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 \fora...

Satbir

3.8k views

Satbir asked Jan 13, 2020

1 votes

0 answers

134

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’??

Represent these two statement in first order logic:$A)$ Only Alligators eat humans$B)$ Every Alligator eats humansIs Every represents $\equiv \exists$and Only represents ...

srestha

558 views

srestha asked May 18, 2019

0 votes

0 answers

135

Discrete Mathematics [Self Doubt]
Is this statement valid: $(\exists x(P(x)\rightarrow Q(x)) )\rightarrow (\exists xP(x)\rightarrow \exists xQ(x))$

Is this statement valid:$(\exists x(P(x)\rightarrow Q(x)) )\rightarrow (\exists xP(x)\rightarrow \exists xQ(x))$

GATE_aspirant_2021

312 views

GATE_aspirant_2021 asked Apr 14, 2019

0 votes

0 answers

136

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

How is option (a) correct? Isn’t Universal quantifier not distributive over union/disjunction.Source: https://cse.buffalo.edu/~rapaport/191/distqfroverandor.html

kaveeshnyk

545 views

kaveeshnyk asked Apr 14, 2019

1 votes

1 answer

137

Kenneth Rosen Edition 7 Exercise 1.4 Question 31 (Page No. 54)
Suppose that the domain of $Q(x,y,z)$ consists of triples $x,y,z,$ where $x=0,1$ or $2$ , $y=0$ or $1,$ and $z=0$ or $1.$ Write out these propositions using disjunctions and conjunctions. $a)$ $\forall y \;\;\;Q(0, y, 0)$ $b)$ $\exists x\; \;\; Q(x, 1, 1)$ $c)$ $\exists z \;¬Q(0, 0, z)$ $d)$ $\exists x\;¬Q(x, 0, 1)$

Suppose that the domain of $Q(x,y,z)$ consists of triples $x,y,z,$ where $x=0,1$ or $2$ , $y=0$ or $1,$ and $z=0$ or $1.$ Write out these propositions using disjunctions ...

Pooja Khatri

559 views

Pooja Khatri asked Mar 18, 2019

68 votes

10 answers

138

GATE CSE 2019 | Question: 35
Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z | x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z | w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ denotes ... of all integers Which of the above sets satisfy $\varphi$? $S_1$ and $S_2$ $S_1$ and $S_3$ $S_2$ and $S_3$ $S_1, S_2$ and $S_3$

Consider the first order predicate formula $\varphi$:$\forall x [ ( \forall z \: z | x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w x) \wedge (\forall z \:...

Arjun

20.2k views

Arjun asked Feb 7, 2019

0 votes

3 answers

139

propositional logic
which of the following is tautology? (¬P^(P->q))->¬q ¬(p->q)->¬q [(¬p^q)^[q->(p->q)]]->¬r Both (B) and(C) please explain in detail how to check for especially for condition (C) Because “r” is only in RHS but not in LHS of this implication.

which of the following is tautology?(¬P^(P->q))->¬q¬(p->q)->¬q[(¬p^q)^[q->(p->q)]]->¬rBoth (B) and(C)please explain in detail how to check for especially for condit...

learner_geek

1.1k views

learner_geek asked Jan 22, 2019

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