Predicate 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...

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

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?

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...

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

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 $$\neg \exists x\left( {\forall y\left( \alpha \right) \wedge \left( {\forall z\left( \beta \right)} \right)} \right)?$$

What is the correct translation of the following statement into mathematical logic? "Some real numbers are rational"

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: $...

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...

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...

Uses Modus ponens $$\left( {A,\,\,A \to B\,|\,\, = B} \right)$$ or resolution to show that the following set is inconsistent: (1) $$Q\left( x \right) \to P\left( x \right)V \sim R\...