which statements are true about x? select three options. $\square x \in b \cup c$ $\square x \in b \cap c$ $\square x \in a \cup c$ $\square x \in a \cap c$ $\square x \in a$

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# Brief Explanations:
1. For $ x \in B \cup C $: The union of $ B $ and $ C $ ($ B \cup C $) includes all elements in $ B $, in $ C $, or in both. Since $ x $ is in the intersection of $ B $ and $ C $ (from the Venn diagram), it is in $ B \cup C $.
2. For $ x \in B \cap C $: The intersection of $ B $ and $ C $ ($ B \cap C $) includes elements in both $ B $ and $ C $. From the Venn diagram, $ x $ is in the region common to $ B $ and $ C $, so $ x \in B \cap C $.
3. For $ x \in A \cup C $: The union of $ A $ and $ C $ ($ A \cup C $) includes all elements in $ A $, in $ C $, or in both. Since $ x $ is in $ C $ (and also in $ B \cap C $), it is in $ A \cup C $.
4. For $ x \in A \cap C $: The intersection of $ A $ and $ C $ ($ A \cap C $) is the region common to $ A $ and $ C $. From the diagram, $ x $ is not in $ A $, so $ x
otin A \cap C $.
5. For $ x \in A $: From the Venn diagram, $ x $ is not in the region of set $ A $, so $ x
otin A $.

# Answer:
- $ x \in B \cup C $
- $ x \in B \cap C $
- $ x \in A \cup C $

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