Quantifiers

For two different persons $x$ and $y$, the predicate $M(x, y)$ denotes that $x$ knows $y$. Consider the following statement. There is a person who does not know anyone else, but th...

Which of the following predicate logic formulae/formula is/are CORRECT representation(s) of the statement: "Everyone has exactly one mother"? The meanings of the predicates used ar...

Which of the following predicate logic formulae/formula is/are CORRECT representation(s) of the statement: "Everyone has exactly one mother"? The meanings of the predicates used ar...

Let $P(x)$ be an arbitrary predicate over the domain of natural numbers. Which ONE of the following statements is TRUE?

Consider two functions of time (t), $$f(t)=0.01\,t^2$$ $$g(t)=4\,t$$ where $$0 Now consider the following two statements : (i) For some $$t > 0,g(t) > f(t)$$. (ii) There exists a $...

Geetha has a conjecture about integers, which is of the form $$\forall x\left( {P(x) \Rightarrow \exists yQ(x,y)} \right)$$, where P is a statement about integers, and Q is a state...

Given below are four statements : Statement 1 : All students are inquisitive. Statement 2 : Some students are inquisitive. Statement 3 : No student is inquisitive. Statement 4 : So...

Which one of the following predicate formulae is NOT logically valid? Note that W is a predicate formula without any free occurrence of x .

Consider the first-order logic sentence $$\varphi \equiv \,\,\,\,\,\,\,\exists s\exists t\exists u\forall v\forall w$$ $$\forall x\forall y\psi \left( {s,t,u,v,w,x,y} \right)$$ whe...

Consider the first-order logic sentence $F: \forall x(\exists y R(x, y))$. Assuming non-empty logical domains, which of the sentences below are implied by $F$? I. $\quad \exists y(...

Which one of the following well-formed formulae in predicate calculus is NOT valid?

Suppose $$𝑈$$ is the power set of the set $$S = \left\{ {1,2,3,4,5,6,} \right\}$$. For any $$T \in U,$$ let $$\left| T \right|$$ denote the number of elements in $$𝑇$$ and $$T'$$...

The CORRECT formula for the sentence, "not all rainy days are cold" is

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 foll...

What is the logical translation of the following statement? "None of my friends are perfect."

Which one of the following is NOT logically equivalent to $$\neg \exists x\left( {\forall y\left( \alpha \right) \wedge \left( {\forall z\left( \beta \right)} \right)} \right)?$$

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\l...

Suppose the predicate $$F(x,y,t)$$ is used to represent the statements that person $$x$$ can fool person $$y$$ at time $$t$$. Which one of the statements below expresses best the m...

Consider the following well-formed formulae: $${\rm I}.$$ $$\,\,\neg \forall x\left( {P\left( x \right)} \right)$$ $${\rm I}{\rm I}.\,\,\,\,\,\,\neg \exists x\left( {P\left( x \rig...

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: $...

Which of the following tuple relational calculus expression(s) is/are equivalent to $$\forall t \in r \left(P\left(t\right)\right)$$? I. $$\neg \exists t \in r \left(P\left(t\right...

Which of the following is the negation of $$$\left[ {\forall x,\alpha \to \left( {\exists y,\beta \to \left( {\forall u,\exists v,\gamma } \right)} \right)} \right]?$$$

Let fsa and $$pda$$ be two predicates such that fsa$$(x)$$ means $$x$$ is a finite state automation, and pda$$(y)$$ means that $$y$$ is a pushdown automation. Let $$equivalent$$ be...

Which of the following first order formulae is logically valid? Here $$\alpha \left( x \right)$$ is a first order formulae with $$x$$ as a free variable, and $$\beta $$ is a first...

Let Graph$$(x)$$ be a predicate which denotes that $$x$$ is a graph. Let Connected$$(x)$$ be a predicate which denotes that $$x$$ is connected. Which of the following first order l...

What is the first order predicate calculus statement equivalent to the following? Every teacher is liked by some student

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: $$$\left( {\exists x} \rig...

Which of the following predicate calculus statements is/are valid?