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The problem is asking for two things:

1. **List the elements of the set \( C \)**: 
   The set \( C \) consists of all prime numbers \( x \) such that \( 1 < x < 20 \).

2. **Find \( n(C') \)**:
   Here, \( n(C') \) represents the cardinality (the number of elements) of the complement of set \( C \), which means the number of integers in the range \( 1 < x < 20 \) that are **not** prime.

Let's break it down:

### Part (i): Elements of \( C \)
Prime numbers between 1 and 20 are:
\[
C = \{2, 3, 5, 7, 11, 13, 17, 19\}
\]

### Part (ii): \( n(C') \)
\( C' \) is the complement of \( C \), meaning the numbers between 1 and 20 that are not prime. These numbers are:
\[
C' = \{4, 6, 8, 9, 10, 12, 14, 15, 16, 18\}
\]
The cardinality of \( C' \), \( n(C') \), is the number of elements in this set:
\[
n(C') = 10
\]

Let me know if you'd like further details or have any questions!

Here are 5 related questions to further your understanding:

1. What defines a prime number?
2. How would you define the complement of a set in mathematical terms?
3. What would be the cardinality of \( C \)?
4. How would you find the complement set of \( C \) if the range changed to \( 1 < x < 50 \)?
5. Can a prime number ever be negative? Why or why not?

**Tip**: When identifying prime numbers, remember that a prime number has exactly two distinct divisors: 1 and itself.

C = {x ∈ Z, x is a prime number, 1 < x < 20}. i. List out the elements of C. ii. Find n(C')

Discover how to list prime numbers between 1 and 20 and calculate the cardinality of the complement of this set. Learn key concepts in set theory, including prime numbers and complements, ideal for students in Grades 6-8.

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