Question #e4125

2 Answers
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.

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/#.