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
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 ?