Question

Question #e4125

Answer 1

Yes.

Explanation:

A function f associates to each element x of its domain
an image y = f(x) in its codomain.

`forall x \in`∅`, exists y \in`∅, such that `y = f(x)`

Suppose by contradiction that the statement above is false.

`exists x \in`∅, such that `forall y \in`∅, `y ne f(x)`

Did you see? There exists "somebody" in the empty set. Who?

Q.E.A.

Answer 2

Yes. It is a function. See explanation.

Explanation:

According to a definition an association `f:X ->Y` is a function if and only if:

`AA_{x in X} EE_{y in Y} f(x)=y`

In the given example the condition is fulfilled. The domain `X` contains only one element - empty set `O/` and the value of the function is also an empty set `O/`.