Let
A={1,2,…,14}
. How many subsets of
A
contain exactly one element (i.e., how many singleton subsets are there)? How many doubleton subsets (containing exactly two elements) are there?

Let's solve this step by step:

### 1. Singleton subsets (containing exactly one element):
A singleton subset is a subset that contains exactly one element from set \( A \). Since \( A = \{ 1, 2, \dots, 14 \} \) contains 14 elements, each element forms its own subset.

Thus, the number of singleton subsets is equal to the number of elements in \( A \), which is:
\[
\text{Number of singleton subsets} = 14
\]

### 2. Doubleton subsets (containing exactly two elements):
A doubleton subset is a subset that contains exactly two elements from set \( A \). The number of ways to choose 2 elements from 14 is given by the combination formula:
\[
\binom{14}{2} = \frac{14 \times 13}{2} = 91
\]

Thus, the number of doubleton subsets is:
\[
\text{Number of doubleton subsets} = 91
\]

### Final Answer:
- Number of singleton subsets: \( 14 \)
- Number of doubleton subsets: \( 91 \)

Would you like further details or clarifications on any of these steps? 

Here are five related questions:
1. How many subsets of \( A \) contain exactly 3 elements?
2. What is the total number of subsets of \( A \)?
3. How many subsets of \( A \) contain at least one element?
4. How many subsets of \( A \) contain an even number of elements?
5. How many subsets of \( A \) contain more than 5 elements?

**Tip**: When working with subsets, combinations (\( \binom{n}{k} \)) are helpful to calculate how many ways you can choose \( k \) elements from \( n \).

Let A = {1, 2, ..., 14}. How many subsets of A contain exactly one element (i.e., how many singleton subsets are there)? How many doubleton subsets (containing exactly two elements) are there?

Explore how to find the number of singleton subsets (exactly 1 element) and doubleton subsets (exactly 2 elements) in a set A containing 14 elements. This combinatorics problem uses the combination formula to calculate subsets and is ideal for students in Grades 9-11.

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