Final answer:
To make the set a function, one of the ordered pairs with '2' as the input must be removed. The ordered pairs (2, 5) and (2, 8) both contain the input '2' with different outputs, so removing either one will fulfill the criteria for the set to be a function.
Step-by-step explanation:
In mathematics, 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. An ordered pair consists of two elements with the first element considered as the input and the second as the output. Looking at the set provided, we have: {(1, 3), (2, 5), (6, 8), (9, 10), (3, 1), (2, 8)}. To determine if the set is a function, we check whether each input corresponds to only one output.
In this set, the input '2' corresponds to two different outputs, '5' and '8'. This violates the definition of a function because a function can only have one output for each distinct input. Therefore, to make this set a function, one of the ordered pairs with the input '2' must be removed. The pairs with '2' as an input are (2, 5) and (2, 8). Removing either one of these pairs will result in a set where each input corresponds to a single output, making it a function.