Let A={r,e,a,s,o,n,i,g}, B={m,a,t,h,e,t,i,c,l} and C= the set of vowels. Calculate:

A∪B∪C
A∩B
Cc

Given the sets:
- \( A = \{ r, e, a, s, o, n, i, g \} \)
- \( B = \{ m, a, t, h, e, t, i, c, l \} \)
- \( C = \) the set of vowels, i.e., \( C = \{ a, e, i, o, u \} \)

Let’s calculate each of the expressions:

### 1. \( A \cup B \cup C \)
The union of sets \( A \), \( B \), and \( C \) includes all elements from each set, without duplicates. So,

\[
A \cup B \cup C = \{ r, e, a, s, o, n, i, g, m, t, h, c, l, u \}
\]

Thus, \( A \cup B \cup C = \{ r, e, a, s, o, n, i, g, m, t, h, c, l, u \} \).

### 2. \( A \cap B \)
The intersection of \( A \) and \( B \) includes only elements that are in both sets. 

\[
A \cap B = \{ e, a, i \}
\]

So, \( A \cap B = \{ e, a, i \} \).

### 3. \( C^c \)
\( C^c \) is the complement of \( C \), meaning it includes all elements in the universal set that are not in \( C \). Assuming the universal set includes only letters in \( A \cup B \), we get:

\[
C^c = \{ r, s, n, g, m, t, h, c, l \}
\]

Thus, \( C^c = \{ r, s, n, g, m, t, h, c, l \} \).

---

Would you like further explanation on any of these steps? 

Here are some related questions to explore:

1. How would the union of two sets change if one set were empty?
2. What happens to the intersection if two sets are disjoint?
3. How does the complement of a set depend on the universal set?
4. What if we add more vowels to set \( C \) – how would \( A \cup B \cup C \) change?
5. Can the union or intersection be associative in set theory, and if so, how?

**Tip:** When calculating the union or intersection of sets, remember to include each unique element only once, and always verify if any elements overlap for intersections.

Let A={r,e,a,s,o,n,i,g}, B={m,a,t,h,e,t,i,c,l} and C= the set of vowels. Calculate: A∪B∪C, A∩B, Cc

Explore set theory concepts in this problem involving sets A, B, and C. Calculate the union, intersection, and complement of these sets with detailed step-by-step explanations. Perfect for students in Grades 9-10 learning set theory.

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