It seems like you've uploaded an image of a mathematical set problem. The question is asking to find the number of elements in a set operation involving complements and intersections.

To analyze the problem:

• Universal set $S$ = {Barnsley, Arsenal, Shildon, Sheffield United, West Ham United, Maroka Swallows, Bidvest Wits, Orlando Pirates, Dumbarten, Lyon}
• Set $A$ = {Shildon, West Ham United, Maroka Swallows, Orlando Pirates}
• Set $B$ = {Barnsley, Arsenal, Shildon}

The task is to find the value of $n(A' \cap B')$, where:

• $A'$ is the complement of set $A$, meaning all elements in the universal set that are not in $A$.
• $B'$ is the complement of set $B$, meaning all elements in the universal set that are not in $B$.
• $A' \cap B'$ represents the intersection of $A'$ and $B'$, which includes the elements that are in neither $A$ nor $B$.

Let's calculate it step-by-step.

1. Find $A'$: The complement of $A$ contains all elements from $S$ except those in $A$, i.e. $A = \{ \text{Shildon, West Ham United, Maroka Swallows, Orlando Pirates} \}$. So, $A' = \{ \text{Barnsley, Arsenal, Sheffield United, Bidvest Wits, Dumbarten, Lyon} \}$.

2. Find $B'$: The complement of $B$ contains all elements from $S$ except those in $B$, i.e. $B = \{ \text{Barnsley, Arsenal, Shildon} \}$. So, $B' = \{ \text{Sheffield United, West Ham United, Maroka Swallows, Bidvest Wits, Orlando Pirates, Dumbarten, Lyon} \}$.

3. Find $A' \cap B'$: The intersection of $A'$ and $B'$ includes the elements that are common to both $A'$ and $B'$. These elements are:
   $A' \cap B' = \{ \text{Sheffield United, Bidvest Wits, Dumbarten, Lyon} \}$.

4. Count the number of elements in $A' \cap B'$:
   There are 4 elements in the intersection.

Thus, $n(A' \cap B') = 4$.

Let me know if you need more details or clarifications on any part of this!

Additional Questions:

1. What does the complement of a set represent in set theory?
2. How do you calculate the union and intersection of two sets?
3. What are some real-world applications of set theory?
4. How do you interpret the cardinality of a set?
5. Can you compute the union of $A$ and $B$ for this example?

Tip: Always start by clearly identifying the universal set and the elements in the sets you’re working with to avoid mistakes in complement calculations.