Question

Express this statement using quantifiers: “Every student in this class has taken some course in every department in the school of mathematical sciences.”

Short answer

The statement can be written using quantifiers is \(\forall x\exists y\forall zE\left( {x,y,z} \right)\).

Step-by-step solution

Introduction

Consider the statement, “In the school of mathematical sciences, each student in the class has taken some course in each department.”

Let \(x\) represents student, \(y\) indicates a course, and \(z\) denotes a department in the school of mathematical sciences.

Quantifiers

Universal quantifier represents for all and denotes the symbol as \(\forall \).

Existential quantifiers represent there exists and denote the symbol as \(\exists \).

Here every student indicates a universal quantifier \(\forall x\).

Some course represents existential quantifier \(\exists y\).

Every department represents a universal quantifier \(\forall z\).

Presentation of statement using quantifiers

The statement can be written using quantifiers is \(\forall x\exists y\forall zE\left( {x,y,z} \right)\),

Here \(E\left( {x,y,z} \right)\) is the statement that each student\(x\)has taken some course\(y\) in each department \(z\).

And the domains are the set of class students, the set of some courses at the school and the set of all school of mathematical sciences departments.