Draw venn diagram showing: (i) AUB CAUC but BEC, (ii) A∩B CA∩C but B¢C.

Here are the Venn diagrams illustrating the given relationships for both parts (i) and (ii):

1. **Part (i)**: \( A \cup B \subseteq C \cup A \cup C \) but \( B \subseteq C \).
   - The union of sets \( A \) and \( B \) is contained within the larger union of \( A \), \( C \), and \( C \), while set \( B \) is fully inside set \( C \).

2. **Part (ii)**: \( A \cap B \subseteq A \cap C \) but \( B \nsubseteq C \).
   - The intersection of sets \( A \) and \( B \) is contained within the intersection of \( A \) and \( C \), but set \( B \) is not fully inside \( C \).

Let me know if you'd like further explanation on these relationships!

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Here are 5 related questions for further exploration:
1. What happens if \( A \subseteq B \) in a similar context?
2. How would the Venn diagram change if \( A \nsubseteq C \)?
3. Can \( A \cup B = A \cup C \) ever occur? Under what conditions?
4. What if \( A \cap B = A \cap C \)? How would the diagram change?
5. What is the significance of symmetric difference in these sets?

**Tip**: Understanding set notation and relationships helps in visualizing and solving complex logical problems in mathematics.

Draw Venn diagram showing: (i) AUB ⊆ AUC but B⊆C, (ii) A∩B ⊆ A∩C but B⊄C.

Explore a detailed Venn diagram illustrating set theory concepts, including the union and intersection of sets and subset relations. Understand how sets A, B, and C relate to each other under the given conditions. Suitable for students in Grades 9-12.

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