In general, if , then . So all the numbers in a given equivalence class will be related in this way.
(d) Think about the rules you are given that make and related:
- Either . In other words, at least one of or and at least one of and must be zero.
- Or . In other words, the product of all four numbers and is positive. So what does this tell you about the individual signs of and ?
Then use the fact that whenever two ordered pairs and are related by one or other of these rules, then they will be in the same equivalence class.
(e) Think of some numbers , for which . E.g. . So all these numbers will be in the same equivalence class.