first-order logic

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 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 predicate formula φ: ∀x[(∀z z|x ⇒ ((z = x) ∨ (z = 1))) ⇒ ∃w (w > x) ∧ (∀z z|w ⇒ ((w = z) ∨ (z = 1)))] Here 'a|b' denotes that 'a divides b', where a and b...

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 is a tautology?

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...

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 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...

Which one of the first order predicate calculus statements given below correctly expresses the following English statement? Tigers and lion attack if they are hungry of threatened.

Consider the following first order logic formula in which $$R$$ is a binary relation symbol. $$\forall x\forall y\left( {R\left( {x,\,y} \right) \Rightarrow R\left( {y,x} \right)}...

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