Hi

I was solving some problem about the set of functions and a doubt came to me (is it correct english ?). Consider function

Consider the case where and

So

Now function is type of a relation, and any subset of is a relation from A to B. Since , and

is a relation from A to B. Now the definition of a function is

which can be written as an implication

since , the antecedent will be FALSE always , so the

implication will be TRUE always, so the condition for the function is satisfied and

we can say the the relation is a function from A to B.

is it correct reasoning ?