Answer
The mathematical expressions of the expression can be written as
$\exists x \exists y[P(x, y) \wedge \forall z(P(z, y) \rightarrow(x=z)) \wedge \forall z(P(x, w) \rightarrow(w=y))]$
Work Step by Step
A step by step solution
Let:
$P(x,y)$= “student $x$ has taken class $y$”
Domain $x$= All student in this class.
Domain $y$= All mathematics classes in this school.
It can be seen in the expression that “there is exactly one student in this class who has taken exactly one mathematics class at the school”,
The class depends on the students.
“Exactly one means that there exists one and that there does not exist another one”
Using the above interpretations, we can then write the statement as a mathematical expression:
$\exists x \exists y[P(x, y) \wedge \forall z(P(z, y) \rightarrow(x=z)) \wedge \forall z(P(x, w) \rightarrow(w=y))]$
