List all subsets or determine the number of subsets as requested.

Determine the number of subsets of {1, 2, 3, ..., 6}

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 \(\{1, 2, 3, 4, 5, 6\}\), there are 6 elements. So, the number of subsets is:

\[
2^6 = 64
\]

Thus, the set \(\{1, 2, 3, 4, 5, 6\}\) has 64 subsets.

Would you like to see how to list these subsets or any further details?

Here are 5 related questions to expand on this topic:
1. How many subsets contain exactly 3 elements from the set \(\{1, 2, 3, 4, 5, 6\}\)?
2. What is the number of proper subsets of \(\{1, 2, 3, 4, 5, 6\}\)?
3. How does the number of subsets change if the set has 7 elements instead of 6?
4. What is the formula for determining the number of subsets of a set with \(n\) elements?
5. How can you calculate the number of subsets that include a specific element of the set?

**Tip**: The number of subsets always includes the empty set and the set itself.

Determine the number of subsets of {1, 2, 3, ..., 6}

Learn how to calculate the number of subsets for the set {1, 2, 3, 4, 5, 6}. Using the formula 2^n, find that a set with 6 elements has 64 subsets. This explanation covers basic concepts in combinatorics and set theory, suitable for students in Grades 6-8.

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