I am having some trouble with this question. I am not sure what to do at this point since the instructor said to ignore the reference to example 2. Below is the questions as they are on the worksheet:
(Ignore the reference to Example 2 as it does not apply)
And Example 2 is:
I am very confused by what is going on here any help would be greatly appreciated.
I think your instructor is trying to say that you don't NEED the example 2 to solve the problem, but the book is noting that those pairs are in the equivalence class of R. So if you look at the (x,y) pairs from example 2, say (1,2) and look out our relation R. So 1 is R related to 2 if and only if 2-1 is an integer. So the pair (1,2) is in the equivalence class.
As for part a) you want to find ALL possible pairs that make your relation true such that x = 1. So start with plug and chug and try to pick up a pattern. I will write out a few to check so you can see 1R1, 1R2. Does 1-1 equal an integer? Yes,it equals 0 Does 1 -2 equal an integer? Yes, it equals -1.
Part b) is a little more tricky when you are trying to consider all possible values, but it is the same idea.
In general you want to consider things like "Is it true if I use negatives? Integers? Rationals? Irrationals?" Then from what makes your relation true you can decide what "type" of numbers are related given your specific relation.