In the provided image, we have two sets, $A$ and $B$, displayed as overlapping circles in a Venn diagram. Each region of the diagram is labeled with different elements: $c, w, p, a, s, m, g, f, h,$ and $n$.

To find $A \oplus B$ (the symmetric difference of $A$ and $B$), we need to identify the elements that belong to either $A$ or $B$, but not to both. In other words, it excludes elements in the intersection of $A$ and $B$ (the area where both sets overlap).

Step 1: Identify the sets

• Set $A$ consists of the elements inside circle $A$: $\{ c, w, p, a, s, m \}$.
• Set $B$ consists of the elements inside circle $B$: $\{ a, s, m, g, f, h \}$.

Step 2: Symmetric difference $A \oplus B$

We exclude the elements that are common to both $A$ and $B$, which are $\{ a, s, m \}$ (these are in the intersection).

Thus, the symmetric difference $A \oplus B$ includes:

• Elements in $A$ but not in $B$: $\{ c, w, p \}$.
• Elements in $B$ but not in $A$: $\{ g, f, h \}$.

Final Answer:

The elements of $A \oplus B$ are: $\{ c, w, p, g, f, h \}$

Would you like further details or clarification?

Related Questions:

1. What is the intersection of sets $A$ and $B$?
2. How would you find $A \cup B$ using the given Venn diagram?
3. Which elements belong exclusively to set $A$ but not $B$?
4. Which elements belong exclusively to set $B$ but not $A$?
5. Can you explain the relationship between $A \cap B$ and $A \oplus B$?

Tip:

The symmetric difference $A \oplus B$ is useful for finding elements that are not shared between two sets. It highlights the unique elements of both sets while excluding the overlap.