Is it possible for a relation that is not a function to have an infinite domain and infinite range? If so,
sketch a possible relation. If not, explain why not.
No, it is not possible for a relation that is not a function to have an infinite domain and infinite range.
A relation is a set of ordered pairs, where each input value in the domain is paired with exactly one output value in the range. In other words, for every input, there can only be one output value.
If a relation is not a function, it means that there exists at least one input value that is paired with more than one output value. In this case, the relation will have a finite range because there are only a finite number of distinct output values.
To have an infinite domain, the relation would need to have infinitely many distinct input values. However, since there are only a finite number of distinct output values, it is impossible for the relation to have an infinite range.
Therefore, it is not possible for a relation that is not a function to have an infinite domain and infinite range.