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Recent questions tagged first-order-logic
26
votes
4
answers
271
TIFR CSE 2010 | Part A | Question: 8
Which of the following is NOT necessarily true? { Notation: The symbol ''$\neg$''notes negation; $P (x, y)$ means that for given $x$ and $y$, the property $P(x, y)$ is true }. $(∀x∀y P(x, y)) \Rightarrow (∀y∀x P(x, y))$ ... $(∃x∀y P(x, y)) \Rightarrow (∀y∃x P(x, y))$ $(∀x∃y P(x, y)) \Rightarrow (∃y∀x P(x, y))$
Which of the following is NOT necessarily true? { Notation: The symbol ''$\neg$''notes negation; $P (x, y)$ means that for given $x$ and $y$, the property $P(x, y)$ is tr...
makhdoom ghaya
3.4k
views
makhdoom ghaya
asked
Oct 2, 2015
Mathematical Logic
tifr2010
mathematical-logic
first-order-logic
+
–
2
votes
2
answers
272
What is the correct representation of the stmt in first-order predicate calculus ?
Given the statement : "Men who are intelligent have knowledge." What is the correct representation of the statement in first-order predicate calculus? $\forall x$ man $(x) \wedge$ intelligent $(x) \rightarrow \exists y$ ... $(x) \wedge$ knowledge $(y) \rightarrow$ have knowledge $(x, y)$ None of the above.
Given the statement : "Men who are intelligent have knowledge."What is the correct representation of the statement in first-order predicate calculus?$\forall x$ man $(x) ...
aayushranjan01
1.8k
views
aayushranjan01
asked
May 14, 2015
Mathematical Logic
mathematical-logic
first-order-logic
+
–
88
votes
5
answers
273
GATE CSE 2015 Set 2 | Question: 55
Which one of the following well-formed formulae is a tautology? $\forall x \, \exists y \, R(x,y) \, \leftrightarrow \, \exists y \, \forall x \, R(x, y)$ ... $\forall x \, \forall y \, P(x,y) \, \rightarrow \, \forall x \, \forall y \, P(y, x)$
Which one of the following well-formed formulae is a tautology? $\forall x \, \exists y \, R(x,y) \, \leftrightarrow \, \exists y \, \forall x \, R(x, y)$$( \forall x \,...
go_editor
21.4k
views
go_editor
asked
Feb 13, 2015
Mathematical Logic
gatecse-2015-set2
mathematical-logic
normal
first-order-logic
+
–
50
votes
9
answers
274
GATE IT 2005 | Question: 36
Let $P(x)$ and $Q(x)$ ...
Let $P(x)$ and $Q(x)$ be arbitrary predicates. Which of the following statements is always TRUE?$\left(\left(\forall x \left(P\left(x\right) \vee Q\left(x\right)\right)\r...
Ishrat Jahan
15.1k
views
Ishrat Jahan
asked
Nov 3, 2014
Mathematical Logic
gateit-2005
mathematical-logic
first-order-logic
normal
+
–
28
votes
2
answers
275
GATE IT 2004 | Question: 3
Let $a(x, y), b(x, y,)$ and $c(x, y)$ be three statements with variables $x$ and $y$ chosen from some universe. Consider the following statement: $\qquad(\exists x)(\forall y)[(a(x, y) \wedge b(x, y)) \wedge \neg c(x, y)]$ ... $\neg (\forall x)(\exists y)[(a(x, y) \vee b(x, y)) \to c(x, y)]$
Let $a(x, y), b(x, y,)$ and $c(x, y)$ be three statements with variables $x$ and $y$ chosen from some universe. Consider the following statement:$\qquad(\exists x)(\foral...
Ishrat Jahan
6.4k
views
Ishrat Jahan
asked
Nov 1, 2014
Mathematical Logic
gateit-2004
mathematical-logic
normal
discrete-mathematics
first-order-logic
+
–
63
votes
7
answers
276
GATE IT 2006 | Question: 21
Consider the following first order logic formula in which $R$ is a binary relation symbol. $∀x∀y (R(x, y) \implies R(y, x))$ The formula is satisfiable and valid satisfiable and so is its negation unsatisfiable but its negation is valid satisfiable but its negation is unsatisfiable
Consider the following first order logic formula in which $R$ is a binary relation symbol.$∀x∀y (R(x, y) \implies R(y, x))$The formula issatisfiable and validsatisfia...
Ishrat Jahan
13.6k
views
Ishrat Jahan
asked
Oct 31, 2014
Mathematical Logic
gateit-2006
mathematical-logic
normal
first-order-logic
+
–
43
votes
5
answers
277
GATE IT 2007 | Question: 21
Which one of these first-order logic formulae is valid? $\forall x\left(P\left(x\right) \implies Q\left(x\right)\right) \implies \left(∀xP\left(x\right)\implies \forall xQ\left(x\right)\right)$ ... $\forall x \exists y P\left(x, y\right)\implies \exists y \forall x P\left(x, y\right)$
Which one of these first-order logic formulae is valid?$\forall x\left(P\left(x\right) \implies Q\left(x\right)\right) \implies \left(∀xP\left(x\right)\implies \forall ...
Ishrat Jahan
10.6k
views
Ishrat Jahan
asked
Oct 29, 2014
Mathematical Logic
gateit-2007
mathematical-logic
normal
first-order-logic
+
–
43
votes
2
answers
278
GATE IT 2008 | Question: 22
Which of the following is the negation of $[∀ x, α → (∃y, β → (∀ u, ∃v, y))]$ $[∃ x, α → (∀y, β → (∃u, ∀ v, y))]$ $[∃ x, α → (∀y, β → (∃u, ∀ v, ¬y))]$ $[∀ x, ¬α → (∃y, ¬β → (∀u, ∃ v, ¬y))]$ $[∃ x, α \wedge (∀y, β \wedge (∃u, ∀ v, ¬y))]$
Which of the following is the negation of $[∀ x, α → (∃y, β → (∀ u, ∃v, y))]$$[∃ x, α → (∀y, β → (∃u, ∀ v, y))]$$[∃ x, α → (∀y, β → ...
Ishrat Jahan
7.9k
views
Ishrat Jahan
asked
Oct 27, 2014
Mathematical Logic
gateit-2008
mathematical-logic
normal
first-order-logic
+
–
68
votes
9
answers
279
GATE IT 2008 | Question: 21
Which of the following first order formulae is logically valid? Here $\alpha(x)$ is a first order formula with $x$ as a free variable, and $\beta$ ... $[(\forall x, \alpha(x)) \rightarrow \beta] \rightarrow [\forall x, \alpha(x) \rightarrow \beta]$
Which of the following first order formulae is logically valid? Here $\alpha(x)$ is a first order formula with $x$ as a free variable, and $\beta$ is a first order formul...
Ishrat Jahan
15.3k
views
Ishrat Jahan
asked
Oct 27, 2014
Mathematical Logic
gateit-2008
first-order-logic
normal
+
–
56
votes
6
answers
280
GATE CSE 2011 | Question: 30
Which one of the following options is CORRECT given three positive integers $x, y$ and $z$ ... always true irrespective of the value of $x$ $P(x)$ being true means that $x$ has exactly two factors other than $1$ and $x$
Which one of the following options is CORRECT given three positive integers $x, y$ and $z$, and a predicate$$P\left(x\right) = \neg \left(x=1\right)\wedge \forall y \left...
go_editor
13.5k
views
go_editor
asked
Sep 29, 2014
Mathematical Logic
gatecse-2011
mathematical-logic
normal
first-order-logic
+
–
37
votes
11
answers
281
GATE CSE 2014 Set 3 | Question: 53
The CORRECT formula for the sentence, "not all Rainy days are Cold" is $\forall d (\text{Rainy}(d) \wedge \text{~Cold}(d))$ $\forall d ( \text{~Rainy}(d) \to \text{Cold}(d))$ $\exists d(\text{~Rainy}(d) \to \text{Cold}(d))$ $\exists d(\text{Rainy}(d) \wedge \text{~Cold}(d))$
The CORRECT formula for the sentence, "not all Rainy days are Cold" is$\forall d (\text{Rainy}(d) \wedge \text{~Cold}(d))$$\forall d ( \text{~Rainy}(d) \to \text{Cold}(d)...
go_editor
8.0k
views
go_editor
asked
Sep 28, 2014
Mathematical Logic
gatecse-2014-set3
mathematical-logic
easy
first-order-logic
+
–
53
votes
8
answers
282
GATE CSE 2013 | Question: 27
What is the logical translation of the following statement? "None of my friends are perfect." $∃x(F (x)∧ ¬P(x))$ $∃ x(¬ F (x)∧ P(x))$ $ ∃x(¬F (x)∧¬P(x))$ $ ¬∃ x(F (x)∧ P(x))$
What is the logical translation of the following statement?"None of my friends are perfect."$∃x(F (x)∧ ¬P(x))$$∃ x(¬ F (x)∧ P(x))$$ ∃x(¬F (x)∧¬P(x))$$ ¬�...
Arjun
14.5k
views
Arjun
asked
Sep 24, 2014
Mathematical Logic
gatecse-2013
mathematical-logic
easy
first-order-logic
+
–
43
votes
8
answers
283
GATE CSE 2007 | Question: 22
Let $\text{ Graph}(x)$ be a predicate which denotes that $x$ is a graph. Let $\text{ Connected}(x)$ be a predicate which denotes that $x$ ... $\forall x \, \Bigl ( \text{ Graph}(x) \implies \lnot \text{ Connected}(x) \Bigr )$
Let $\text{ Graph}(x)$ be a predicate which denotes that $x$ is a graph. Let $\text{ Connected}(x)$ be a predicate which denotes that $x$ is connected. Which of the follo...
Kathleen
9.1k
views
Kathleen
asked
Sep 21, 2014
Mathematical Logic
gatecse-2007
mathematical-logic
easy
first-order-logic
+
–
50
votes
4
answers
284
GATE CSE 2005 | Question: 41
What is the first order predicate calculus statement equivalent to the following? "Every teacher is liked by some student" $∀(x)\left[\text{teacher}\left(x\right) → ∃(y) \left[\text{student}\left(y\right) → \text{likes}\left(y,x\right)\right]\right]$ ...
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) → ∃...
gatecse
11.9k
views
gatecse
asked
Sep 21, 2014
Mathematical Logic
gatecse-2005
mathematical-logic
easy
first-order-logic
+
–
71
votes
5
answers
285
GATE CSE 2010 | Question: 30
Suppose the predicate $F(x, y, t)$ is used to represent the statement that person $x$ can fool person $y$ at time $t$. Which one of the statements below expresses best the meaning of the formula, $\qquad∀x∃y∃t(¬F(x,y,t))$ Everyone can ... time No one can fool everyone all the time Everyone cannot fool some person all the time No one can fool some person at some time
Suppose the predicate $F(x, y, t)$ is used to represent the statement that person $x$ can fool person $y$ at time $t$.Which one of the statements below expresses best the...
gatecse
82.5k
views
gatecse
asked
Sep 21, 2014
Mathematical Logic
gatecse-2010
mathematical-logic
easy
first-order-logic
+
–
89
votes
7
answers
286
GATE CSE 2004 | Question: 23, ISRO2007-32
Identify the correct translation into logical notation of the following assertion. Some boys in the class are taller than all the girls Note: $\text{taller} (x, y)$ is true if $x$ is taller than $y$ ... $(\exists x) (\text{boy}(x) \land (\forall y) (\text{girl}(y) \rightarrow \text{taller}(x, y)))$
Identify the correct translation into logical notation of the following assertion.Some boys in the class are taller than all the girlsNote: $\text{taller} (x, y)$ is true...
Kathleen
132k
views
Kathleen
asked
Sep 18, 2014
Mathematical Logic
gatecse-2004
mathematical-logic
easy
isro2007
first-order-logic
+
–
54
votes
6
answers
287
GATE CSE 2006 | Question: 26
Which one of the first order predicate calculus statements given below correctly expresses the following English statement? Tigers and lions attack if they are hungry or threatened. ...
Which one of the first order predicate calculus statements given below correctly expresses the following English statement? Tigers and lions attack if they are hungry or ...
Rucha Shelke
9.4k
views
Rucha Shelke
asked
Sep 18, 2014
Mathematical Logic
gatecse-2006
mathematical-logic
normal
first-order-logic
+
–
116
votes
6
answers
288
GATE CSE 2003 | Question: 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: ... I_1\) does not Neither \(I_1\) nor \(I_2\) satisfies \(\alpha\) Both \(I_1\) and \(I_2\) satisfies \(\alpha\)
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...
Kathleen
16.2k
views
Kathleen
asked
Sep 16, 2014
Mathematical Logic
gatecse-2003
mathematical-logic
difficult
first-order-logic
+
–
59
votes
7
answers
289
GATE CSE 2003 | Question: 32
Which of the following is a valid first order formula? (Here \(\alpha\) and \(\beta\) are first order formulae with $x$ as their only free variable) $((∀x)[α] ⇒ (∀x)[β]) ⇒ (∀x)[α ⇒ β]$ $(∀x)[α] ⇒ (∃x)[α ∧ β]$ $((∀x)[α ∨ β] ⇒ (∃x)[α]) ⇒ (∀x)[α]$ $(∀x)[α ⇒ β] ⇒ (((∀x)[α]) ⇒ (∀x)[β])$
Which of the following is a valid first order formula? (Here \(\alpha\) and \(\beta\) are first order formulae with $x$ as their only free variable)$((∀x)[α] ⇒ (∀x...
Kathleen
17.0k
views
Kathleen
asked
Sep 16, 2014
Mathematical Logic
gatecse-2003
mathematical-logic
first-order-logic
normal
+
–
28
votes
7
answers
290
GATE CSE 2009 | Question: 26
Consider the following well-formed formulae: $\neg \forall x(P(x))$ $\neg \exists x(P(x))$ $\neg \exists x(\neg P(x))$ $\exists x(\neg P(x))$ Which of the above are equivalent? $\text{I}$ and $\text{III}$ $\text{I}$ and $\text{IV}$ $\text{II}$ and $\text{III}$ $\text{II}$ and $\text{IV}$
Consider the following well-formed formulae:$\neg \forall x(P(x))$$\neg \exists x(P(x))$$\neg \exists x(\neg P(x))$$\exists x(\neg P(x))$Which of the above are equivalent...
gatecse
5.7k
views
gatecse
asked
Sep 15, 2014
Mathematical Logic
gatecse-2009
mathematical-logic
normal
first-order-logic
+
–
40
votes
8
answers
291
GATE CSE 2009 | Question: 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$ ... $\forall x((G(x) \vee S(x)) \implies P(x))$
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: ...
gatecse
8.7k
views
gatecse
asked
Sep 15, 2014
Mathematical Logic
gatecse-2009
mathematical-logic
easy
first-order-logic
+
–
37
votes
6
answers
292
GATE CSE 2014 Set 1 | Question: 1
Consider the statement "Not all that glitters is gold Predicate glitters$(x)$ is true if $x$ glitters and predicate gold$(x)$ is true if $x$ ... $\exists x: \text{glitters}(x)\wedge \neg \text{gold}(x)$
Consider the statement "Not all that glitters is gold”Predicate glitters$(x)$ is true if $x$ glitters and predicate gold$(x)$ is true if $x$ is gold. Which one of the ...
gatecse
6.8k
views
gatecse
asked
Sep 15, 2014
Mathematical Logic
gatecse-2014-set1
mathematical-logic
first-order-logic
+
–
71
votes
5
answers
293
GATE CSE 2008 | Question: 30
Let $\text{fsa}$ and $\text{pda}$ be two predicates such that $\text{fsa}(x)$ means $x$ is a finite state automaton and $\text{pda}(y)$ means that $y$ is a pushdown automaton. Let $\text{equivalent}$ ...
Let $\text{fsa}$ and $\text{pda}$ be two predicates such that $\text{fsa}(x)$ means $x$ is a finite state automaton and $\text{pda}(y)$ means that $y$ is a pushdown autom...
Kathleen
14.4k
views
Kathleen
asked
Sep 12, 2014
Mathematical Logic
gatecse-2008
easy
mathematical-logic
first-order-logic
+
–
78
votes
6
answers
294
GATE CSE 1992 | Question: 92,xv
Which of the following predicate calculus statements is/are valid? $(\forall (x)) P(x) \vee (\forall(x))Q(x) \implies (\forall (x)) (P(x) \vee Q(x))$ $(\exists (x)) P(x) \wedge (\exists (x))Q(x) \implies (\exists (x)) (P(x) \wedge Q(x))$ ... $(\exists (x)) (P(x) \vee Q(x)) \implies \sim (\forall (x)) P(x) \vee (\exists (x)) Q(x)$
Which of the following predicate calculus statements is/are valid?$(\forall (x)) P(x) \vee (\forall(x))Q(x) \implies (\forall (x)) (P(x) \vee Q(x))$$(\exists (x)) P(x) \w...
Arjun
16.8k
views
Arjun
asked
Sep 2, 2014
Mathematical Logic
gate1992
mathematical-logic
normal
first-order-logic
+
–
46
votes
3
answers
295
GATE CSE 2013 | Question: 47
Which one of the following is NOT logically equivalent to $¬∃x(∀ y (α)∧∀z(β ))$ ? $∀ x(∃ z(¬β )→∀ y(α))$ $∀x(∀ z(β )→∃ y(¬α))$ $∀x(∀ y(α)→∃z(¬β ))$ $∀x(∃ y(¬α)→∃z(¬β ))$
Which one of the following is NOT logically equivalent to $¬∃x(∀ y (α)∧∀z(β ))$ ?$∀ x(∃ z(¬β )→∀ y(α))$$∀x(∀ z(β )→∃ y(¬α))$$∀x(∀ y(�...
gatecse
12.1k
views
gatecse
asked
Aug 21, 2014
Mathematical Logic
mathematical-logic
normal
marks-to-all
gatecse-2013
first-order-logic
+
–
33
votes
4
answers
296
GATE CSE 2012 | Question: 13
What is the correct translation of the following statement into mathematical logic? “Some real numbers are rational” $\exists x (\text{real}(x) \lor \text{rational}(x))$ $\forall x (\text{real}(x) \to \text{rational}(x))$ $\exists x (\text{real}(x) \wedge \text{rational}(x))$ $\exists x (\text{rational}(x) \to \text{real}(x))$
What is the correct translation of the following statement into mathematical logic?“Some real numbers are rational”$\exists x (\text{real}(x) \lor \text{rational}(x))...
gatecse
8.9k
views
gatecse
asked
Aug 5, 2014
Mathematical Logic
gatecse-2012
mathematical-logic
easy
first-order-logic
+
–
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