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∈A∧b∈B} 4口，1①，43，t夏，30Q0 Jun Ma (majungnju.edu.cn)1-9 Set Theory (II):Relations 2021年12月02日3/52. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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? Jun Ma (majun@nju.edu.cn) 1-9 Set Theory (II): Relations 2021 年 12 月 02 日 3 / 52