Given the set $A = \{ a, b, \{a, c\}, \emptyset \}$, we will solve each part of the problem:

Part (a): $A - \{a, c\}$

The set $\{a, c\}$ is an element of $A$, so we need to remove it from $A$:

$A = \{ a, b, \{a, c\}, \emptyset \}$

Removing $\{a, c\}$ from $A$:

$A - \{a, c\} = \{ a, b, \{a, c\}, \emptyset \} - \{ \{a, c\} \} = \{ a, b, \emptyset \}$

Part (b): $A - \{ \{a, b\} \}$

The set $\{a, b\}$ is not an element of $A$, so $A$ remains unchanged:

$A - \{ \{a, b\} \} = \{ a, b, \{a, c\}, \emptyset \}$

Part (c): $\emptyset - A$

The set difference of any set $B$ with the empty set $\emptyset$ is always $\emptyset$:

$\emptyset - A = \emptyset$

Part (d): $\{a, c\} - A$

Here, $\{a, c\}$ is not an element but a subset of $A$. We find the difference by removing the elements of $A$ that are in $\{a, c\}$:

Since neither $a$ nor $c$ are elements of $A$:

$\{a, c\} - A = \{a, c\}$

Summary of Results:

a) $A - \{a, c\} = \{ a, b, \emptyset \}$

b) $A - \{ \{a, b\} \} = \{ a, b, \{a, c\}, \emptyset \}$

c) $\emptyset - A = \emptyset$

d) $\{a, c\} - A = \{a, c\}$

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Do you want any further details or have any questions?

Here are some additional questions to expand on this topic:

1. What is the result of $A - \{b\}$?
2. How would you describe the difference between set difference and subset?
3. What is the union of $A$ and $\{d, e\}$?
4. If $B = \{a, b\}$, what is $A \cup B$?
5. What is the intersection of $A$ and $\{a, \{a, c\}\}$?
6. How does the presence of $\emptyset$ affect set operations?
7. What is the complement of $A$ if the universal set is $\{a, b, c, d, \{a, c\}, \emptyset\}$?
8. How do nested sets like $\{a, c\}$ complicate set operations?

Tip: When performing set operations, always check if the elements involved are subsets or individual elements to avoid confusion.