Help with Relations and Functions?

Question

I'm currently doing work on discrete mathematics in my free time and am having some difficulties with understanding some questions pertaining to Relations and Functions. To be specific, I'm stuck on the following practice question:

We have a relation R on Z+ defined as follows:
mRn if and only if m|n.
a. Explain why the relation R is not a function.
b. Determine the set A = {m ∈ Z|mR52} and give its cardinality |A|.

How would I go about finding the results of A and B to satisfy the relations? Any help is greatly appreciated! Thanks.

Answer 1

HINT:

A relation is functional only if the following holds: $$\forall x,y_1,y_2 \in R(xRy_1 \wedge xRy_2) \Rightarrow y_1 = y_2$$

Answer 2

a) The definition of a function relationship, xRy if you use their notation, is that each x has only one related y. If the relation is m|n, do any of the m have more than one n related to it? What is y if 3Ry? Is there more than one?

[Not really hint. If we used the common f(x) notations would f(n) = m s.t. n|m even make sense? What is f(3)?]

b) The set is all m that divide 52. How many are there and what are they?