Proof: We must show that R is reflexive, symmetric and transitive.
{"Image DocumentName": "Proof: We must show that R is reflexive, symmetric and transitive.", "Image ImageDescription": "Let R be the relation on the set of ordered pairs of positive integers such that ((a,b), (c,d))\uf0ceR iff ad=bc. Is R an equivalence relation? Proof: We must show that R is reflexive, symmetric and transitive. Transitive: We must show that if ((a,b), (c,d))\uf0ceR and ((c,d), (e,f)) \uf0ceR, then ((a,b),(e,f) \uf0ceR. Assume that ((a,b), (c,d))\uf0ceR and ((c,d), (e,f)) \uf0ceR. Then ad = cb and cf = de. This implies that a/b = c/d and that c/d = e/f, so a/b = e/f which means that af = be. Therefore ((a,b),(e,f)) \uf0ceR. (remember we are using positive integers.) Positive integers because a/b and (-a)/(-b) would work equally well. Therefore, can\u2019t distinguish between positive and negative pairs.", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}