Express the Statement "There is exactly one student in this class who has taken exactly one mathematics class at this school" using the uniqueness quantifier. Then express this statement using quantifiers, without using the uniqueness quantifier.

Step1:

We have to express the given statement “There is exactly one student in this class who has taken exactly one mathematics class at this school" using the uniqueness quantifier. Then express this statement using quantifiers, without using the uniqueness quantifier”.

Step 2: First we have to find the elements which represent the qualifier expression

Suppose

a -student

b- class

c-mathematics class

d-school

Statement in parts -There is exactly one student )

In this class

one mathematics class(

At this school (

As we know Uniqueness quantifier:

let’s consider

has free variable x( no others)

“There exist exactly one x such that

So, we can write: (x=y)