1. **State the problem:** We are given two sets $A = \{1, \{2\}, \{1,2\}\}$ and $B = \{1, \{1,2,3\}\}$. We need to find the symmetric difference $A \Delta B$. 2. **Recall the formula:** The symmetric difference of two sets $A$ and $B$ is defined as: $$ A \Delta B = (A \setminus B) \cup (B \setminus A) $$ This means elements in $A$ or $B$ but not in both. 3. **Find $A \setminus B$:** Elements in $A$ not in $B$. - $1$ is in both $A$ and $B$, so exclude. - $\{2\}$ is in $A$ but not in $B$. - $\{1,2\}$ is in $A$ but not in $B$. So, $A \setminus B = \{\{2\}, \{1,2\}\}$. 4. **Find $B \setminus A$:** Elements in $B$ not in $A$. - $1$ is in both, exclude. - $\{1,2,3\}$ is in $B$ but not in $A$. So, $B \setminus A = \{\{1,2,3\}\}$. 5. **Combine to get $A \Delta B$:** $$ A \Delta B = \{\{2\}, \{1,2\}\} \cup \{\{1,2,3\}\} = \{\{2\}, \{1,2\}, \{1,2,3\}\} $$ **Final answer:** $$ A \Delta B = \{\{2\}, \{1,2\}, \{1,2,3\}\} $$