Define a relation on R\{0} (that is, the set of real numbers with 0 removed) as follows: ~ "~y" means that EQ. (Recall that is the set of rational numbers.) Prove (using the format demonstrated in class) that is an equivalence relation on R\{0}. Write up a nice version of your argument instead of submitting scratch work. (CAUTION: The prescription that "Q" is NOT meant to imply that x and y must be integers-or even that they must be rational! For instance, we have 2~32-check this using the definition!-even though 2 and 32 are both irrational.) Prove the following: For any positive integer a and any integers x and n, if x =, n, then ged(a, n) |x.