4. Let A = R, and let N be the relation on A given by x N y if xy 2 0. Prove that N is not an equivalence relation. 5. Fix an integer M > 0, and dene a relation NM on Z by 0: NM b if M|b a. Prove that NM is an equivalence relation. 6. (a) LetA = Fun(IR>0, R>0), the set of functions from R>0 to R>o. Dene a relation onA by f N g if limx_,m f (x) / g(x) converges to a (nite) limit L > 0. Prove that N is an equivalence relation. (You are free to use any limit rules you've learned without proof). (b) Is 2x2 6 [x2]? Is x E [6"]? Provide a short justication