Axiomatic Systems, finding a relation

Question

I am currently taking Axiomatic Systems and I am struggling with this chapter of material. One of the homework questions is: "Let A = {3,17,29,45} and B = {4,6, 22,60}. A relation R from A to B is defined by aRb if and only if a + b is a prime. i) Find the relation R. ii) Is R a function from A to B?" But I do not know how to even begin to approach this question.

Answer 1

There are $4 \times 4=16$ ordered pairs of one element from A and one from B with the A element first. These are candidates for elements of your relation. As an example, $3R4$ because $3+4=7$ and $7$ is prime, so $(3,4)$ is one element of the relation. Go through the rest of the pairs and check them. That will give you the relation $R$. Now apply the definition of a function that you quoted to answer the second part.