Subjects set theory

Set Complement Intersection D72669

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Question: Use the Venn diagram to determine the set $A' \cap B$.
1. **State the problem:** We need to find the elements in the set $A' \cap B$, which means the elements that are in $B$ but not in $A$. 2. **Recall definitions:** - $A'$ (the complement of $A$) contains all elements not in $A$. - $A' \cap B$ means elements that are in $B$ and also not in $A$. 3. **Analyze the Venn diagram:** - Elements in $A$ only: $\$, $%$ - Elements in $A \cap B$: $\Delta$ - Elements in $B$ only: $3$, $6$, $9$ - Elements outside both $A$ and $B$: $12$, $02$ 4. **Find $A' \cap B$:** - These are elements in $B$ but not in $A$, so exclude $\Delta$ (intersection). - The elements are $3$, $6$, $9$. 5. **Final answer:** $$A' \cap B = \{3,6,9\}$$