I'm a little confused on these problems as far as the wording goes. I know how to tell if one is reflexive, symmetric, or transitive.
The way the problem is set up is:
A= the set of all positive integers. R = {(x,y)} | x and y are prime
Do I strictly use prime numbers to test this out?
OR could I use 1 since it says " The set of all positive integers" and 1 is a positive integer?
How could I read this to make it "easier" to understand?
$A$ acts on the set of positive integers, so reflexivity requires that every positive integer relates to itself, or for $x \in A, R(x,x)$. Hopefully, you can find a counterexample.
Similarly, symmetry requires that for all $x,y \in A, R(x,y) \to R(y,x)$, and transitivity is defined as usual, acting on all elements on $A$. From there, you should be able to tell why $R$ is transitive and symmetric.