Question

A function is a relation if and only if the x-values do not repeat in a given set.

Answer 1

This statement is true. In a relation, the x-values can repeat, meaning that for different y-values there may be the same x-value. However, in a function, each x-value must correspond to exactly one y-value. Therefore, if the x-values do not repeat in a given set, it satisfies the definition of a function.