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.