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.