Question #e4125

2 Answers
Vinícius Ferraz
Dec 28, 2016

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.

Daniel L.
Dec 28, 2016

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/.

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