To find the subsets of a set $A = \{a, b, c, d\}$, we can use the following process:

Subset Formula

The total number of subsets of a set with $n$ elements is given by $2^n$. In this case, $A$ has 4 elements, so the number of subsets is:

$2^4 = 16$

Thus, $A = \{a, b, c, d\}$ has 16 subsets, including the empty set and the set itself. The subsets are as follows:

List of Subsets:

1. $\emptyset$ (the empty set)
2. $\{a\}$
3. $\{b\}$
4. $\{c\}$
5. $\{d\}$
6. $\{a, b\}$
7. $\{a, c\}$
8. $\{a, d\}$
9. $\{b, c\}$
10. $\{b, d\}$
11. $\{c, d\}$
12. $\{a, b, c\}$
13. $\{a, b, d\}$
14. $\{a, c, d\}$
15. $\{b, c, d\}$
16. $\{a, b, c, d\}$ (the set itself)

Summary

The set $A = \{a, b, c, d\}$ has 16 subsets, which include the empty set, single-element subsets, two-element subsets, three-element subsets, and the entire set itself.

Would you like further details or examples on how to compute subsets, or explore related concepts?

Here are some follow-up questions:

1. How do you compute the subsets of a set with more than 4 elements?
2. What is the difference between subsets and proper subsets?
3. How are power sets related to subsets?
4. Can subsets be non-contiguous, and if so, how do we handle them?
5. How can subsets be useful in combinatorics and probability?

Tip: The subsets of a set always include the empty set and the set itself, and the total number of subsets is $2^n$, where $n$ is the number of elements in the set.