Final answer:
Discrete sets are considered as collections with countable elements, which can be either finite or infinite but distinct and separately countable. Continuous elements, which can take on any value within a range and be subdivided infinitely, are not inherent to discrete sets. Examples in different contexts help clarify the nature of discrete versus continuous data. Option B is correct.
Step-by-step explanation:
Discrete sets in a given context are considered as collections of items that can be counted individually. These items are distinct and separate; they can't be subdivided into smaller parts that belong to the set. There are some key concepts related to discrete sets:
Finite elements refer to a set that contains a limited number of elements. An example would be the set of all students in a classroom.
Countable elements are part of a set that can be counted one by one. This can include infinite sets as well, such as the set of all integers, which is not finite but still countable.
Infinite elements describe a set that has an unlimited number of elements. However, not all infinite sets are considered discrete. For example, the set of all points on a line segment is infinite but continuous, not discrete.
Continuous elements are not characteristic of discrete sets. Continuous data can take on any value within a range and can be subdivided infinitely.
Looking at various contexts:
Number of books purchased is quantitative discrete because you count books individually.
The total amount paid for books is quantitative continuous because the amount can vary continuously across a range.
The number of times per week is quantitative discrete since you count occurrences in whole numbers.
Duration or amount of time is quantitative continuous, as it can be measured with any degree of precision within a range.