x- yis an assignment, meaning the value of x becomes the same as that of y. Given that the X = {0, 1, 2, 3), Y = {0, 1, 2, 3), and f = {(0,1),(1,0),(2,0),(3,3)}, answer the following parts: You are to minimize changes to X, Y, and f, to answer the other parts, maximize info of nfl and minimize |f Ufuf, ufgl. In the first three parts of your answer, specify only the changed f, X, and/or Y. Also include a short explanation why you make the changes. If a set is not changed, do not mention it in your answer. There is no need to use subscript in your answer, for example, f, can be written as fo. 1. start with fo f,X7 -- X, Y, Y, make minimal changes potentially to fo, X, and/or Yo so that fo : X, Y is an injection but not a surjection. Put your answer here: 2. start with f, - f,X, X,Y, Y, make minimal changes potentially to f., X, and/or Y, so that f : X, Y is a surjection but not an injection. Put your answer here: 3. start with fg f,X, X,Y, Y, make minimal changes potentially to f2, X, and/or Yso that fy : X - Y is a bijection. Put your answer here: 4. what is in fenfnf? Put your answer here: 5. what is fu fuf, U f? Put your answer here: 6. what is f, -p? Put your answer here: 7. evaluate 3a e f (Wb ef, (a + b)) and briefly explain your answer regardless of the result of the evaluation Put your answer here: x- yis an assignment, meaning the value of x becomes the same as that of y. Given that the X = {0, 1, 2, 3), Y = {0, 1, 2, 3), and f = {(0,1),(1,0),(2,0),(3,3)}, answer the following parts: You are to minimize changes to X, Y, and f, to answer the other parts, maximize info of nfl and minimize |f Ufuf, ufgl. In the first three parts of your answer, specify only the changed f, X, and/or Y. Also include a short explanation why you make the changes. If a set is not changed, do not mention it in your answer. There is no need to use subscript in your answer, for example, f, can be written as fo. 1. start with fo f,X7 -- X, Y, Y, make minimal changes potentially to fo, X, and/or Yo so that fo : X, Y is an injection but not a surjection. Put your answer here: 2. start with f, - f,X, X,Y, Y, make minimal changes potentially to f., X, and/or Y, so that f : X, Y is a surjection but not an injection. Put your answer here: 3. start with fg f,X, X,Y, Y, make minimal changes potentially to f2, X, and/or Yso that fy : X - Y is a bijection. Put your answer here: 4. what is in fenfnf? Put your answer here: 5. what is fu fuf, U f? Put your answer here: 6. what is f, -p? Put your answer here: 7. evaluate 3a e f (Wb ef, (a + b)) and briefly explain your answer regardless of the result of the evaluation Put your answer here
