F = {(x, y ) | x + y = 10}

Question

Select either relation (if the set is a relation but not a function), function (if the set is both a relation and a function), or neither (if the set is not a relation).

Answer 1

As I understand it, a function maps the elements of one set on to the elements of another set. Here, F is a set of pairs of numbers whose sum is 10. F is an infinite set because there is no mention of what sets x and y belong to (e.g, integers, natural numbers, real numbers, etc.). I think it's neither a relation nor a function. x+y=10 is a linear function (mapping x to y or vice versa) but this function is an internal requirement of its elements, not a function itself.