FTCE General Knowledge Math Practice Test

How would you describe the term 'distinct elements' in a set?

1. Elements that are all the same

2. Elements that include duplicates

3. Elements that are unique

4. Elements that are ordered

The correct answer is: Elements that are unique

The term 'distinct elements' in a set refers to elements that are unique, meaning that no element is repeated within that set. When a set has distinct elements, each item is different from the others, which ensures that there are no duplicates present. This concept is fundamental in set theory, as it allows for the identification and grouping of unique items, leading to a clearer understanding of relationships and operations involving sets. In contrast, having all the same elements refers to a scenario where there is no variety, which does not align with the definition of distinctness. Including duplicates directly contradicts the idea of being distinct, as it implies that some elements are repeated. Lastly, ordering elements is related to sequences or lists rather than sets; sets are inherently unordered collections. Therefore, recognizing the unique nature of distinct elements is crucial in mathematical discussions regarding sets.