https://file.aiquickdraw.com/mathbot/file/1729618637942sximf4b5.jpg

The image you uploaded shows a Venn diagram with two intersecting sets. The sets include the following values:

- The left circle contains numbers 16 (outside the intersection) and 8 (inside the intersection).
- The right circle contains numbers 19 (outside the intersection) and 8 (inside the intersection).
- Outside both circles, there is the number 20, which represents elements outside the union of the sets.

You have two questions labeled as:
- (a) \( n(M \cup C) \)
- (b) \( n(C') = 36 \)

Here's how to interpret and solve the questions:

### (a) \( n(M \cup C) \) — Union of the sets
The union \( M \cup C \) means all elements that are in either set \( M \) or set \( C \), including those in the intersection. To find this, we sum all the elements inside both circles:

- Left circle (set \( M \)): 16 (outside intersection) and 8 (in the intersection).
- Right circle (set \( C \)): 19 (outside intersection) and 8 (in the intersection).

So, the total number of elements in \( M \cup C \) is:
\[
n(M \cup C) = 16 + 8 + 19 = 43
\]

### (b) \( n(C') = 36 \) — Complement of set \( C \)
The complement of set \( C \), denoted as \( C' \), represents all elements that are not in set \( C \). From the diagram, the elements outside \( C \) include the number outside the entire Venn diagram, which is 20, and the elements in the left circle that are not in the right circle (which is 16).

Thus, the total number of elements in \( C' \) is:
\[
n(C') = 16 + 20 = 36
\]
This is consistent with the value given in the problem.

Would you like more details on how the Venn diagram and sets were analyzed, or any other part of the solution? 

Here are five related questions you might find helpful:
1. How do we calculate the intersection of two sets in a Venn diagram?
2. What does the complement of a set represent in set theory?
3. How do we find the total number of elements in a universal set?
4. How can Venn diagrams help in visualizing probability problems?
5. What is the principle of inclusion and exclusion in set theory?

**Tip:** In Venn diagrams, remember that the sum of all regions inside the circles must equal the total number of elements when working within a universal set.

Use the Venn diagram below to fill the missing statement.

Solve a Venn diagram problem involving the union and complement of sets. This problem includes two questions: calculating n(M ∪ C) and determining n(C'). A clear breakdown of set theory concepts such as the union, intersection, and complement is provided. Suitable for students in Grades 9-10.

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