Please tell me what I'm doing wrong

(1 point) Order 10 of the following sentences so that they form a logical proof of the statement: For A = Zx Z, define a relation R on A by: (a,b), (c,d)) ER = ad = be Prove that R is an equivalence relation on A. Choose from these statements Hence, R is symmetric since ((a,b),(a, b)) E R A logical proof of the given proposition. Consider ((a,b), (c,d)) ER. Then ad=bc = bc = ad and so (c,d)R(a,b). Consider ((a,b), (c,d)) E R. Hence R is reflexive. Hence R is symmetric. Next consider (a, b)R(c,d) and (c,d)R(e, f) Hence R is symmetric. Next consider (a, b)R(c,d) and (c,d)R(e, f) Then, ad = bc and cf = de and so af = be. af = be =(a,b)R(e, f) (a, b)R(c,d) Bab = cd Then ad=bc = bc = ad and so (c,d)R(a,b). af = be (a,b)R(e, f) Define Ron Zx Z such that ((a,b), (c,d)) ER #ad=bc Hence, R is transitive. For any (a,b), ab = ba. Therefore (a, b)R(a,b) Hence, R is transitive. For any (a,b), ab=ba. Hence R is reflexive. Hence, R is reflexive and (a, b)R(c,d) means R is symmetric and transitive. Thus R is an equivalence relation. (a,b)R(c,d) = ab = cd. Nathan is a goob Then, ad=bc and cf = de and so af = be. Therefore (a, b)R(a,b) Thus R is an equivalence relation