7/9 7. Predicates and Quantifiers Online Quiz Questions

Which description best defines a predicate?

The statement $\exists x\,P(x)$ means that at least one object in the domain makes $P(x)$ true.

What is the standard term for the collection of objects that a variable may represent in a discussion?

Let $S(x)$ mean “$x$ is a student” and $P(x)$ mean “$x$ is present,” with the domain consisting of all people. Which formula translates “Every student is present”?

Which statements correctly describe evidence for quantified claims? Select all that apply.

True or false: In the formula $\forall x\,P(x)$, the variable $x$ is bound.

What is the status of the variable $x$ in the unquantified expression $P(x)$?

Let $L(x,y)$ mean “$x$ likes $y$.” Which formula translates “There is someone whom everyone likes”?

Let $D(x)$ mean “$x$ is a dog” and $R(x)$ mean “$x$ is a reptile.” Which formulas correctly express “No dogs are reptiles”? Select all that apply.

Explain how to negate $\forall x\,P(x)$. Give the equivalent symbolic form and an ordinary-language interpretation.

Let the domain be the integers and let $E(x)$ mean $x>0$. What is the truth value of $E(-3)$?

Assume the domain is all people. Let $S(x)$ mean “$x$ is a student” and $A(x)$ mean “$x$ submitted the assignment.” Which formula correctly translates “Every student submitted the assignment”?

Let $S(x)$ mean “$x$ is a student” and $P(x)$ mean “$x$ passed the exam.” Which formula correctly translates “Some student passed the exam”?

Let $L(x,y)$ mean “$x$ likes $y$.” What does $\forall x\,\exists y\,L(x,y)$ mean?

Which formula is logically equivalent to $\neg\forall x\,P(x)$?

True or false: $\exists x\,P(x)$ means that exactly one object in the domain satisfies $P(x)$.

In the formula $\forall x\,P(x)$, what is the technical term for the variable $x$?

What is the technical term for an object that demonstrates that $\exists x\,P(x)$ is true?