Answer to Question #242198 in Discrete Mathematics for lyn

Question

I. Use quantifiers to express the following statements.

1. Every student enrolls in a math class.

2. There is a student in a class who drops a math course.

3. Every student in this class wears an ID.

4. At least one student in this class requests for uniform pass.

5. Every student access the free wifi connection in the campus.

Answer 1

1.Let $x$ - is a student and $P(x)$ - student enrolls in a math class.

So 'Every student enrolls in a math class' is $\forall x P(x).$

2.Let $x$ - is a student and $P(x)$ - student is in a class, $Q(x)$ - a student drops a math course

So 'There is a student in a class who drops a math course' is $\exist x P(x)\land Q(x)$.

3.Let $x$ - is a student and $P(x)$ - student is in a class, $Q(x)$ - a student  wears an ID.

So 'Every student in this class wears an ID.' is $\forall x P(x) \mapsto Q(x)$.

4.Let $x$ - is a student and $P(x)$ - student is in this class, $Q(x)$ - a student  requests for uniform pass.

So 'At least one student in this class requests for uniform pass' is $\exist x P(x)\land Q(x)$ .

5.Let $x$ - is a student and $P(x)$ - student is in the campus, $Q(x)$ - a student access the free wifi connection.

So 'Every student access the free wifi connection in the campus' is $\forall x P(x) \mapsto Q(x).$