Definition (Relations) A relation R from A to B is a subset of A x B: RCAXB Definition(Cartesian Products) The Cartesian product A x B of A and B is defined as A×B≌{(a,b)|a∈AAb∈B} Axiom (Ordered Pairs) (a,b)=(c,d)→a=c∧b=d 4口，1①，43，t夏，3080 Hengfeng Wei (hfweixinju.edu.cn) 1-9 Set Theory (II):Relations 2019年12月03日5/51. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition (Relations) A relation R from A to B is a subset of A × B: R ⊆ A × B Definition (Cartesian Products) The Cartesian product A × B of A and B is defined as A × B ≜ {(a, b) | a ∈ A ∧ b ∈ B} Axiom (Ordered Pairs) (a, b) = (c, d) ⇐⇒ a = c ∧ b = d Q : Are you satisfied with the definitions above? Hengfeng Wei (hfwei@nju.edu.cn) 1-9 Set Theory (II): Relations 2019 年 12 月 03 日 5 / 51