Question

Order 5 of the following sentences so that they form a logical sequence of subsets:

Choose from these sets
[Mtn. Dew, Sprite)
(Coke, Mtn. Dew, Dr. Pepper)
[Coke, Mm. Dew, Sprite, Dr. Pepper)
[Sprite)
[Mtn. Dew]
(Dr. Pepper)
[Coke, Sprite]
[Coke, Sprite, Dr. Pepper)

Sets from smallest to largest ordered by inclusion.

Answer 1

Ordering sets by subset inclusion involves listing sets from smallest to largest, ensuring that each set contains all elements of the previous set. We start with individual soda brands and end with the set that includes all mentioned brands.

Step-by-step explanation:

To order the given sets by subset inclusion from smallest to largest, we'll look for sets that are completely contained within other sets. Note that brackets {} indicate a set, and a set that is a subset of another will have all of its elements included in the larger set.

1. \( \{Sprite\} \)
2. \( \{Mtn. Dew\} \)
3. \( \{Dr. Pepper\} \)
4. \( \{Coke, Sprite\} \)
5. \( \{Coke, Sprite, Dr. Pepper\} \)
6. \( \{Coke, Mtn. Dew, Dr. Pepper\} \)
7. \( \{Coke, Mtn. Dew, Sprite, Dr. Pepper\} \)

Each subsequent set in the list includes all elements of the preceding sets, fulfilling the requirement for a logical sequence. For instance, the set with just 'Sprite' is included in the set with 'Coke and Sprite', which in turn is included in the set with 'Coke, Sprite, and Dr. Pepper', and so on, until the largest set which contains all possible items.