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Recent questions tagged first-order-logic
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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.
aayushranjan01
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Mathematical Logic
May 14, 2015
by
aayushranjan01
1.7k
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mathematical-logic
first-order-logic
88
votes
5
answers
272
GATE CSE 2015 Set 2 | Question: 55
Which one of the following well-formed formulae is a tautology? $\forall x \, \exists y \, R(x,y) \, \leftrightarrow \, \exists y \, \forall x \, R(x, y)$ ... $\forall x \, \forall y \, P(x,y) \, \rightarrow \, \forall x \, \forall y \, P(y, x)$
go_editor
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in
Mathematical Logic
Feb 13, 2015
by
go_editor
21.0k
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gatecse-2015-set2
mathematical-logic
normal
first-order-logic
50
votes
9
answers
273
GATE IT 2005 | Question: 36
Let $P(x)$ and $Q(x)$ ...
Ishrat Jahan
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in
Mathematical Logic
Nov 3, 2014
by
Ishrat Jahan
14.9k
views
gateit-2005
mathematical-logic
first-order-logic
normal
28
votes
2
answers
274
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: $\qquad(\exists x)(\forall y)[(a(x, y) \wedge b(x, y)) \wedge \neg c(x, y)]$ ... $\neg (\forall x)(\exists y)[(a(x, y) \vee b(x, y)) \to c(x, y)]$
Ishrat Jahan
asked
in
Mathematical Logic
Nov 1, 2014
by
Ishrat Jahan
6.3k
views
gateit-2004
mathematical-logic
normal
discrete-mathematics
first-order-logic
62
votes
6
answers
275
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
Ishrat Jahan
asked
in
Mathematical Logic
Oct 31, 2014
by
Ishrat Jahan
13.4k
views
gateit-2006
mathematical-logic
normal
first-order-logic
42
votes
5
answers
276
GATE IT 2007 | Question: 21
Which one of these first-order logic formulae is valid? $\forall x\left(P\left(x\right) \implies Q\left(x\right)\right) \implies \left(∀xP\left(x\right)\implies \forall xQ\left(x\right)\right)$ ... $\forall x \exists y P\left(x, y\right)\implies \exists y \forall x P\left(x, y\right)$
Ishrat Jahan
asked
in
Mathematical Logic
Oct 29, 2014
by
Ishrat Jahan
10.4k
views
gateit-2007
mathematical-logic
normal
first-order-logic
43
votes
2
answers
277
GATE IT 2008 | Question: 22
Which of the following is the negation of $[∀ x, α → (∃y, β → (∀ u, ∃v, y))]$ $[∃ x, α → (∀y, β → (∃u, ∀ v, y))]$ $[∃ x, α → (∀y, β → (∃u, ∀ v, ¬y))]$ $[∀ x, ¬α → (∃y, ¬β → (∀u, ∃ v, ¬y))]$ $[∃ x, α \wedge (∀y, β \wedge (∃u, ∀ v, ¬y))]$
Ishrat Jahan
asked
in
Mathematical Logic
Oct 27, 2014
by
Ishrat Jahan
7.7k
views
gateit-2008
mathematical-logic
normal
first-order-logic
68
votes
9
answers
278
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 $\beta$ ... $[(\forall x, \alpha(x)) \rightarrow \beta] \rightarrow [\forall x, \alpha(x) \rightarrow \beta]$
Ishrat Jahan
asked
in
Mathematical Logic
Oct 27, 2014
by
Ishrat Jahan
15.1k
views
gateit-2008
first-order-logic
normal
55
votes
6
answers
279
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 $x$
go_editor
asked
in
Mathematical Logic
Sep 29, 2014
by
go_editor
13.2k
views
gatecse-2011
mathematical-logic
normal
first-order-logic
37
votes
11
answers
280
GATE CSE 2014 Set 3 | Question: 53
The CORRECT formula for the sentence, "not all Rainy days are Cold" is $\forall d (\text{Rainy}(d) \wedge \text{~Cold}(d))$ $\forall d ( \text{~Rainy}(d) \to \text{Cold}(d))$ $\exists d(\text{~Rainy}(d) \to \text{Cold}(d))$ $\exists d(\text{Rainy}(d) \wedge \text{~Cold}(d))$
go_editor
asked
in
Mathematical Logic
Sep 28, 2014
by
go_editor
7.8k
views
gatecse-2014-set3
mathematical-logic
easy
first-order-logic
52
votes
8
answers
281
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))$
Arjun
asked
in
Mathematical Logic
Sep 24, 2014
by
Arjun
14.1k
views
gatecse-2013
mathematical-logic
easy
first-order-logic
43
votes
8
answers
282
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 $x$ ... $\forall x \, \Bigl ( \text{ Graph}(x) \implies \lnot \text{ Connected}(x) \Bigr )$
Kathleen
asked
in
Mathematical Logic
Sep 21, 2014
by
Kathleen
8.9k
views
gatecse-2007
mathematical-logic
easy
first-order-logic
50
votes
4
answers
283
GATE CSE 2005 | Question: 41
What is the first order predicate calculus statement equivalent to the following? "Every teacher is liked by some student" $∀(x)\left[\text{teacher}\left(x\right) → ∃(y) \left[\text{student}\left(y\right) → \text{likes}\left(y,x\right)\right]\right]$ ...
gatecse
asked
in
Mathematical Logic
Sep 21, 2014
by
gatecse
11.7k
views
gatecse-2005
mathematical-logic
easy
first-order-logic
69
votes
5
answers
284
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
gatecse
asked
in
Mathematical Logic
Sep 21, 2014
by
gatecse
70.1k
views
gatecse-2010
mathematical-logic
easy
first-order-logic
87
votes
7
answers
285
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 $y$ ... $(\exists x) (\text{boy}(x) \land (\forall y) (\text{girl}(y) \rightarrow \text{taller}(x, y)))$
Kathleen
asked
in
Mathematical Logic
Sep 18, 2014
by
Kathleen
111k
views
gatecse-2004
mathematical-logic
easy
isro2007
first-order-logic
54
votes
6
answers
286
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. ...
Rucha Shelke
asked
in
Mathematical Logic
Sep 18, 2014
by
Rucha Shelke
9.2k
views
gatecse-2006
mathematical-logic
normal
first-order-logic
113
votes
6
answers
287
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 \(\alpha\)
Kathleen
asked
in
Mathematical Logic
Sep 16, 2014
by
Kathleen
15.8k
views
gatecse-2003
mathematical-logic
difficult
first-order-logic
59
votes
7
answers
288
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) $((∀x)[α] ⇒ (∀x)[β]) ⇒ (∀x)[α ⇒ β]$ $(∀x)[α] ⇒ (∃x)[α ∧ β]$ $((∀x)[α ∨ β] ⇒ (∃x)[α]) ⇒ (∀x)[α]$ $(∀x)[α ⇒ β] ⇒ (((∀x)[α]) ⇒ (∀x)[β])$
Kathleen
asked
in
Mathematical Logic
Sep 16, 2014
by
Kathleen
16.9k
views
gatecse-2003
mathematical-logic
first-order-logic
normal
28
votes
7
answers
289
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 $\text{IV}$
gatecse
asked
in
Mathematical Logic
Sep 15, 2014
by
gatecse
5.5k
views
gatecse-2009
mathematical-logic
normal
first-order-logic
40
votes
8
answers
290
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 $P(x): x$ ... $\forall x((G(x) \vee S(x)) \implies P(x))$
gatecse
asked
in
Mathematical Logic
Sep 15, 2014
by
gatecse
8.4k
views
gatecse-2009
mathematical-logic
easy
first-order-logic
37
votes
6
answers
291
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 $x$ ... $\exists x: \text{glitters}(x)\wedge \neg \text{gold}(x)$
gatecse
asked
in
Mathematical Logic
Sep 15, 2014
by
gatecse
6.6k
views
gatecse-2014-set1
mathematical-logic
first-order-logic
70
votes
5
answers
292
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 $\text{equivalent}$ ...
Kathleen
asked
in
Mathematical Logic
Sep 12, 2014
by
Kathleen
14.1k
views
gatecse-2008
easy
mathematical-logic
first-order-logic
78
votes
6
answers
293
GATE CSE 1992 | Question: 92,xv
Which of the following predicate calculus statements is/are valid? $(\forall (x)) P(x) \vee (\forall(x))Q(x) \implies (\forall (x)) (P(x) \vee Q(x))$ $(\exists (x)) P(x) \wedge (\exists (x))Q(x) \implies (\exists (x)) (P(x) \wedge Q(x))$ ... $(\exists (x)) (P(x) \vee Q(x)) \implies \sim (\forall (x)) P(x) \vee (\exists (x)) Q(x)$
Arjun
asked
in
Mathematical Logic
Sep 2, 2014
by
Arjun
16.4k
views
gate1992
mathematical-logic
normal
first-order-logic
45
votes
3
answers
294
GATE CSE 2013 | Question: 47
Which one of the following is NOT logically equivalent to $¬∃x(∀ y (α)∧∀z(β ))$ ? $∀ x(∃ z(¬β )→∀ y(α))$ $∀x(∀ z(β )→∃ y(¬α))$ $∀x(∀ y(α)→∃z(¬β ))$ $∀x(∃ y(¬α)→∃z(¬β ))$
gatecse
asked
in
Mathematical Logic
Aug 21, 2014
by
gatecse
11.9k
views
mathematical-logic
normal
marks-to-all
gatecse-2013
first-order-logic
33
votes
4
answers
295
GATE CSE 2012 | Question: 13
What is the correct translation of the following statement into mathematical logic? “Some real numbers are rational” $\exists x (\text{real}(x) \lor \text{rational}(x))$ $\forall x (\text{real}(x) \to \text{rational}(x))$ $\exists x (\text{real}(x) \wedge \text{rational}(x))$ $\exists x (\text{rational}(x) \to \text{real}(x))$
gatecse
asked
in
Mathematical Logic
Aug 5, 2014
by
gatecse
8.6k
views
gatecse-2012
mathematical-logic
easy
first-order-logic
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