Definition (Relations) A relation R from A to B is a subset of A x B: RCAXB If A B,R is called a relation on A. 4口，1①，43，t夏，30Q0 Hengfeng Wei (hfweiinju.edu.cn)1-9 Set Theory (II):Relations 2019年12月03日10/51
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition (Relations) A relation R from A to B is a subset of A × B: R ⊆ A × B If A = B, R is called a relation on A. Definition (Notations) (a, b) ∈ R R(a, b) aRb Hengfeng Wei (hfwei@nju.edu.cn) 1-9 Set Theory (II): Relations 2019 年 12 月 03 日 10 / 51
Definition (Relations) A relation R from A to B is a subset of A x B: RCAXB If A B,R is called a relation on A. Definition (Notations) (a,b)∈R R(a,b) aRb 4口·￥①，43，t夏，里Q0 Hengfeng Wei (hfweixinju.edu.cn) 1-9 Set Theory (II):Relations 2019年12月03日10/51
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition (Relations) A relation R from A to B is a subset of A × B: R ⊆ A × B If A = B, R is called a relation on A. Definition (Notations) (a, b) ∈ R R(a, b) aRb Hengfeng Wei (hfwei@nju.edu.cn) 1-9 Set Theory (II): Relations 2019 年 12 月 03 日 10 / 51
Definition (Relations) A relation R from A to B is a subset of A x B: RCAXB Examples Hengfeng Wei (hfweiinju.edu.cn)1-9 Set Theory (II):Relations 2019年12月03日11/51
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition (Relations) A relation R from A to B is a subset of A × B: R ⊆ A × B Examples ▶ Both A × B and ∅ are relations from A to B. ▶ < = {(a, b) ∈ R × R | a is less than b} ▶ D = {(a, b) ∈ N × N | ∃q ∈ N : a · q = b} ▶ P : the set of people M = {(a, b) ∈ P × P | a is the mother of b} B = {(a, b) ∈ P × P | a is the brother of b} Hengfeng Wei (hfwei@nju.edu.cn) 1-9 Set Theory (II): Relations 2019 年 12 月 03 日 11 / 51
Definition (Relations) A relation R from A to B is a subset of A x B: RCAXB Examples Both A x B and 0 are relations from A to B. Hengfeng Wei (hfweiinju.edu.cn)1-9 Set Theory (II):Relations 2019年12月03日11/51
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition (Relations) A relation R from A to B is a subset of A × B: R ⊆ A × B Examples ▶ Both A × B and ∅ are relations from A to B. ▶ < = {(a, b) ∈ R × R | a is less than b} ▶ D = {(a, b) ∈ N × N | ∃q ∈ N : a · q = b} ▶ P : the set of people M = {(a, b) ∈ P × P | a is the mother of b} B = {(a, b) ∈ P × P | a is the brother of b} Hengfeng Wei (hfwei@nju.edu.cn) 1-9 Set Theory (II): Relations 2019 年 12 月 03 日 11 / 51
Definition (Relations) A relation R from A to B is a subset of A x B: RCAXB Examples Both A x B and 0 are relations from A to B. <={(a,b)∈R×R|a is less than b} Hengfeng Wei (hfweiinju.edu.cn)1-9 Set Theory (II):Relations 2019年12月03日11/51
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition (Relations) A relation R from A to B is a subset of A × B: R ⊆ A × B Examples ▶ Both A × B and ∅ are relations from A to B. ▶ < = {(a, b) ∈ R × R | a is less than b} ▶ D = {(a, b) ∈ N × N | ∃q ∈ N : a · q = b} ▶ P : the set of people M = {(a, b) ∈ P × P | a is the mother of b} B = {(a, b) ∈ P × P | a is the brother of b} Hengfeng Wei (hfwei@nju.edu.cn) 1-9 Set Theory (II): Relations 2019 年 12 月 03 日 11 / 51