Problem 4.22. Five basic properties of binary relations R : A-> B are: 1. R is a surjection1 in 2...
Problem 4.22. Five basic properties of binary relations R : A-> B are: 1. R is a surjection1 in 2. R is an injection [S 1 in] 3. R is a function 1 out 4. R is total1 out] 5. R is empty0 out] Below are some assertions about R. For each assertion, indicate all the properties above that the relation R must have. For example, the first assertion impllies that R is a total surjection. Variables a, a1.... range over A and b, b,... range over B (a) Va Vb. a R b (b) NOT(Va Vb. a R b) (c) Va Vb. NOT(a R b) (d) Va 3b. a R b (f) R is a bijection (g) Ya3b1 a R bl Лу b. a R b IMPLIES b-b1 "mcs"-2017/6/5-19:42-page 121-#129 .5. Finite Cardinality (i) Vbi, b2,a. (a R bi AND a R b2) IMPLIES b-b2 (j) Vai, a2, b. (ai R b AND a2 R b) IMPLIES aia2
Problem 4.22. Five basic properties of binary relations R : A-> B are: 1. R is a surjection1 in 2. R is an injection [S 1 in] 3. R is a function 1 out 4. R is total1 out] 5. R is empty0 out] Below are some assertions about R. For each assertion, indicate all the properties above that the relation R must have. For example, the first assertion impllies that R is a total surjection. Variables a, a1.... range over A and b, b,... range over B (a) Va Vb. a R b (b) NOT(Va Vb. a R b) (c) Va Vb. NOT(a R b) (d) Va 3b. a R b (f) R is a bijection (g) Ya3b1 a R bl Лу b. a R b IMPLIES b-b1 "mcs"-2017/6/5-19:42-page 121-#129 .5. Finite Cardinality (i) Vbi, b2,a. (a R bi AND a R b2) IMPLIES b-b2 (j) Vai, a2, b. (ai R b AND a2 R b) IMPLIES aia2