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Recent questions tagged first-order-logic

0 votes
2 answers
1
Which one is the correct translation of the following statement into mathematical logic? “None of my friends are perfect.” $\neg\:\exists\:x(p(x)\land q(x))$ $\exists\:x(\neg\:p(x)\land q(x))$ $\exists\:x(\neg\:p(x)\land\neg\:q(x))$ $\exists\:x(p(x)\land\neg\:q(x))$
asked Mar 30 in Mathematical Logic Lakshman Patel RJIT 83 views
1 vote
2 answers
2
The first order logic (FOL) statement $((R\vee Q)\wedge(P\vee \neg Q))$ is equivalent to which of the following? $((R\vee \neg Q)\wedge(P\vee \neg Q)\wedge (R\vee P))$ $((R\vee Q)\wedge(P\vee \neg Q)\wedge (R\vee P))$ $((R\vee Q)\wedge(P\vee \neg Q)\wedge(R\vee \neg P))$ $((R\vee Q)\wedge(P\vee \neg Q)\wedge (\neg R\vee P))$
asked Mar 24 in Discrete Mathematics jothee 165 views
1 vote
0 answers
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’??
asked May 18, 2019 in Mathematical Logic srestha 131 views
0 votes
0 answers
4
Is this statement valid: $(\exists x(P(x)\rightarrow Q(x)) )\rightarrow (\exists xP(x)\rightarrow \exists xQ(x))$
asked Apr 14, 2019 in Mathematical Logic GATE_aspirant_2021 73 views
0 votes
0 answers
5
How is option (a) correct? Isn’t Universal quantifier not distributive over union/disjunction. Source: https://cse.buffalo.edu/~rapaport/191/distqfroverandor.html
asked Apr 14, 2019 in Mathematical Logic kaveeshnyk 109 views
0 votes
0 answers
6
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. $a)$ $\forall y \;\;\;Q(0, y, 0)$ $b)$ $\exists x\; \;\; Q(x, 1, 1)$ $c)$ $\exists z \;¬Q(0, 0, z)$ $d)$ $\exists x\;¬Q(x, 0, 1)$
asked Mar 18, 2019 in Mathematical Logic Pooja Khatri 44 views
21 votes
9 answers
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
asked Feb 7, 2019 in Mathematical Logic Arjun 7.4k views
0 votes
3 answers
8
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.
asked Jan 22, 2019 in Mathematical Logic learner_geek 168 views
2 votes
1 answer
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? $q \rightarrow (r \vee s )$ $(q \rightarrow r) \vee s$
asked Jan 7, 2019 in Mathematical Logic Mk Utkarsh 128 views
0 votes
0 answers
11
2 votes
0 answers
12
∀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 ?
asked Dec 23, 2018 in Mathematical Logic Shamim Ahmed 38 views
1 vote
2 answers
14
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 $q \vee s$ $q \vee r$ $\neg q \wedge s$
asked Dec 18, 2018 in Mathematical Logic Arjun 441 views
1 vote
0 answers
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.
asked Dec 6, 2018 in Mathematical Logic Soumya29 107 views
0 votes
0 answers
16
Some cat are intelligent express into first order logic if domain are animals
asked Nov 12, 2018 in Mathematical Logic amit166 48 views
0 votes
0 answers
17
0 votes
1 answer
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
asked Nov 9, 2018 in Mathematical Logic Prince Sindhiya 249 views
0 votes
0 answers
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?!
asked Sep 28, 2018 in Mathematical Logic iarnav 170 views
1 vote
0 answers
24
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
asked Sep 27, 2018 in Mathematical Logic Balaji Jegan 76 views
0 votes
0 answers
25
Twin primes are pairs of numbers pp and p+2p+2 such that both are primes-for instance, 5 and 7, 11 and 13, 41 and 43. The Twin Prime Conjecture says that there are infinitely many twin primes. Let TwinPrime(n)TwinPrime(n) be a predicate that is true if nn and n+2n+2 ... (TwinPrime(n)) ∃m.∀n.n≤m∃m.∀n.n≤m implies TwinPrime(n) ∀m.∃n.n≤m∀m.∃n.n≤m and TwinPrime(n) ∃m.∀n.∃m.∀n. TwinPrime(n) implies n≤m
asked Sep 17, 2018 in Mathematical Logic Kuldeep Pal 40 views
0 votes
0 answers
27
Consider the following statement where parent(x,y) means x is a parent of y. Which of the following statement is true about above first order logic statement ? A. Ramu has at least one parent B. Ramu has at least two parents C. Ramu has at most one parent D. Ramu has at most two parents
asked Sep 8, 2018 in Mathematical Logic Sandy Sharma 131 views
0 votes
0 answers
28
Minesweeper is a single-player computer game invented by Robert Donner in 1989. A unary predicate mine, where mine(x) means that the cell x contains a mine Which of the following statements is the correct interpretation of the above formula? A. There are exactly n mines in the game B. There are at least n mines in the game C. There are at most n mines in the game D. None of the above
asked Sep 8, 2018 in Mathematical Logic Sandy Sharma 85 views
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