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 $n$.