Definition (Relations) A relation R from A to B is a subset of A x B: RCAXB 4口，1①，43，t夏，30Q0 Jun iE jtmomjtedn.cn 1-9 Set Theory (II):Relations 2021 1202 8/52
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 Jun Ma (majun@nju.edu.cn) 1-9 Set Theory (II): Relations 2021 年 12 月 02 日 8 / 52
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 Jun i jumcmjtedn.cn 1-9 Set Theory (II):Relations 2021 1202 8/52
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 Jun Ma (majun@nju.edu.cn) 1-9 Set Theory (II): Relations 2021 年 12 月 02 日 8 / 52
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 Jun Ma (majunainju.edu.cn) 1-9 Set Theory(I):Relations2021年12月02日 8/52
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 Jun Ma (majun@nju.edu.cn) 1-9 Set Theory (II): Relations 2021 年 12 月 02 日 8 / 52
Definition (Relations) A relation R from A to B is a subset of A x B: RCAXB Examples Jun Ma (majungnju.edu.cn)1-9 Set Theory (II):Relations 2021年12月02日 9/52
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition (Relations) A relation R from A to B is a subset of A × B: R ⊆ A × B Examples I Both A × B and ∅ are relations from A to B. I < = {(a, b) ∈ R × R | a is less than b} I D = {(a, b) ∈ N × N | ∃q ∈ N : a · q = b} I 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} Jun Ma (majun@nju.edu.cn) 1-9 Set Theory (II): Relations 2021 年 12 月 02 日 9 / 52
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. Jun Ma (majungnju.edu.cn)1-9 Set Theory (II):Relations 2021年12月02日 9/52
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition (Relations) A relation R from A to B is a subset of A × B: R ⊆ A × B Examples I Both A × B and ∅ are relations from A to B. I < = {(a, b) ∈ R × R | a is less than b} I D = {(a, b) ∈ N × N | ∃q ∈ N : a · q = b} I 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} Jun Ma (majun@nju.edu.cn) 1-9 Set Theory (II): Relations 2021 年 12 月 02 日 9 / 52