# Recent questions tagged first-order-logic

1
Which one is the correct translation of the following statement into mathematical logic? “None of my friends are perfect.” $\neg\:\exists\:x(p(x)\land q(x))$ $\exists\:x(\neg\:p(x)\land q(x))$ $\exists\:x(\neg\:p(x)\land\neg\:q(x))$ $\exists\:x(p(x)\land\neg\:q(x))$
1 vote
2
The first order logic (FOL) statement $((R\vee Q)\wedge(P\vee \neg Q))$ is equivalent to which of the following? $((R\vee \neg Q)\wedge(P\vee \neg Q)\wedge (R\vee P))$ $((R\vee Q)\wedge(P\vee \neg Q)\wedge (R\vee P))$ $((R\vee Q)\wedge(P\vee \neg Q)\wedge(R\vee \neg P))$ $((R\vee Q)\wedge(P\vee \neg Q)\wedge (\neg R\vee P))$
1 vote
3
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’??
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Is this statement valid: $(\exists x(P(x)\rightarrow Q(x)) )\rightarrow (\exists xP(x)\rightarrow \exists xQ(x))$
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How is option (a) correct? Isn’t Universal quantifier not distributive over union/disjunction. Source: https://cse.buffalo.edu/~rapaport/191/distqfroverandor.html
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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. $a)$ $\forall y \;\;\;Q(0, y, 0)$ $b)$ $\exists x\; \;\; Q(x, 1, 1)$ $c)$ $\exists z \;¬Q(0, 0, z)$ $d)$ $\exists x\;¬Q(x, 0, 1)$
7
Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z \mid x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z \mid w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ ... $S3:$ Set of all integers Which of the above sets satisfy $\varphi$? S1 and S2 S1 and S3 S2 and S3 S1, S2 and S3
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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.
1 vote
9
Pardon for the screenshot though. No idea of latex.
10
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? $q \rightarrow (r \vee s )$ $(q \rightarrow r) \vee s$
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∀x(∀z(β)→∃y(¬α)) ⟹∀x(¬∀z(β)∨∃y(¬α)) ⟹¬∃x¬(¬∀z(β)∨∃y(¬α)) ⟹¬∃x(∀z(β)∧¬∃y(¬α)) ⟹¬∃x(∀z(β)∧∀y(α)) In the third line why 2 negations are used ?
1 vote
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1 vote
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Let $\varphi$ be a propositional formula on a set of variables $A$ and $\varphi$ be a propositional formula on a set of variables $B$ , such that $\varphi$ $\Rightarrow$ $\psi$ . A $\textit{Craig interpolant}$ of $\varphi$ and $\psi$ is a propositional formula $\mu$ ... is a Craig interpolant for $\varphi$ and $\psi$ ? $q$ $\varphi$ itself $q \vee s$ $q \vee r$ $\neg q \wedge s$
1 vote
15
Que. Consider domain is the set of all people in the world. $F(x,y) =x \text{ is the friend of y}.$ Represent each of the following sentences using first-order logic statements $1.$ Every person has $at most \ 2$ friends. $2.$ Every person has $exactly \ 2$ friends. $3.$ Every ... $3. \forall x \exists y_1\exists y_2(F(x,y_1) \wedge F(x,y_2) \wedge (y_1 \neq y_2))$ Please verify.
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Some cat are intelligent express into first order logic if domain are animals
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Its answer is a) but here more(x,y) is given means it should be like this -- x is more than y then isn't a) is wrong
18
How to write the last line of Qno. 19 - irrespective of whether the system has been armed the alarm should go off when there is fire For Qno 20 I am getting iii) and iv) as true but answer is a) please check the 5th one
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1)How to do question no. 34,36
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I am getting b) but right option is a) please check it
21
Answer for this is a) but m getting d) as right option please check it
22
answer for this is A) My doubt is why D) can't be the answer
23
Hello, please kindly tell from where to study topic FIRST ORDER LOGIC? Also, list out the topics which are needed to be studied from topic FIRST ORDER LOGIC?!
1 vote
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Some people are Time Travelers and some people are not Time Travelers. P(x) = x is a Person T(x) = x is a Time Traveler Which is/are correct and why? (∀x)(P(x) $\rightarrow$(T(x)∨~T(x))) (∃x)(P(x)^T(x)) ∨ (∃x)(P(x)^~T(x)) (∃x)(P(x)^T(x)) ^ (∃x)(P(x)^~T(x)) (∀x)((P(x)$\rightarrow$T(x)) ∨ (P(x)$\rightarrow$~T(x))) P(x) (∀x)P (∀x)P(x) P