Let X3 1 2 3 4 and y3 1 2 3 4 5 Using the formal definitio

Let X_3 = {1, 2, 3, 4} and y_3 = {1, 2, 3, 4, 5}. Using the formal definition of a function, determine which of the following subsets of X_3 times Y_3 correspond to functions of X_3 rightarrow Y_3. Justify your answer by providing reasons why each is or is not a function. (a) f = {(1.4), (2, 3), (1, 2), (3, 1), (4, 1)} (b) f = {(1, 0), (2, 1), (3, 1)} (c) f = {(1, 0), (2, 1), (3, 1), (4, 2), (1, 0)}

Solution

Definition of Function : A Function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

(3a) Since there are two outputs of input as 1 which are (1,4) and (1,2) . Hence , by definition it is not a function

(3b) Since each input has only one output , hence it is a function

(3c) Since each input has only one output , hence it is a function