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The problem asks to find a set that is:

1. A *proper superset* of set \( A = \{2, 3, 4\} \), meaning it must contain all elements of \( A \) plus at least one additional element.
2. A *subset* of set \( B = \{1, 2, 3, 4, 5\} \), meaning it can only contain elements from \( B \).

### Solution Steps:
- Set \( A = \{2, 3, 4\} \) is given.
- Set \( B = \{1, 2, 3, 4, 5\} \) is also given.
  
To meet both conditions:
1. The new set must include all elements of \( A \) (i.e., \( 2, 3, 4 \)).
2. It must include at least one more element from \( B \) that is not already in \( A \). The possible additional elements from \( B \) are \( 1 \) and \( 5 \).

### Possible Solution:
- One valid set would be \( \{1, 2, 3, 4\} \). This is a proper superset of \( A \) (since it contains all elements of \( A \) and one additional element, \( 1 \)), and it is a subset of \( B \).
- Another valid set could be \( \{2, 3, 4, 5\} \), which is also a proper superset of \( A \) and a subset of \( B \).

Thus, two valid answers are:
- \( \{1, 2, 3, 4\} \)
- \( \{2, 3, 4, 5\} \)

Would you like further clarification or more details on how proper supersets and subsets work?

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Here are 5 related questions you might find helpful:
1. What is the difference between a subset and a proper subset?
2. Can a set be a proper subset and a superset at the same time?
3. What is the power set of a given set?
4. How many proper subsets can be formed from a set with \( n \) elements?
5. How can we determine the union and intersection of two sets?

**Tip:** When finding proper supersets, always check if there are extra elements that belong to the larger set but are not in the smaller set.

Misal diberikan himpunan A = {2, 3, 4} dan B = {1, 2, 3, 4, 5}. Berikanlah sebuah himpunan yang merupakan proper superset dari A sekaligus juga merupakan subset dari himpunan B!

Learn how to find a set that is a proper superset of set A = {2, 3, 4} and also a subset of set B = {1, 2, 3, 4, 5}. Understand the concept of proper supersets and subsets in set theory with this problem, suitable for students in Grades 9-11.

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