To determine the number of subsets of a set, you can use the formula:

\[
\text{Number of subsets} = 2^n
\]

where \(n\) is the number of elements in the set.

For the set \(\{3, 4, 5, 6, 7\}\), the number of elements is \(n = 5\).

Thus, the number of subsets is:

\[
2^5 = 32
\]

So, you're correct: there are 32 subsets of the set \(\{3, 4, 5, 6, 7\}\), which include both the empty set and the set itself.

Do you need more details or have any questions?

Here are 5 related questions:
1. How many proper subsets can be formed from \(\{3, 4, 5, 6, 7\}\)?
2. What is the difference between proper subsets and subsets?
3. How many subsets does a set with 6 elements have?
4. Can a set have infinite subsets if it contains an infinite number of elements?
5. What is a power set and how does it relate to subsets?

**Tip:** The empty set is always considered a subset of any set, even if the set is empty.

Learn how to calculate the number of subsets for the set {3, 4, 5, 6, 7} using the formula 2^n, where n is the number of elements in the set. This example covers essential concepts from set theory, including subsets and power sets. Suitable for students in Grades 6-8.

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