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Let's break down and calculate the cardinality of each set based on the given conditions.

### 6. \( T = \{x \mid 34 < x < 45\} \)

The values of \(x\) must be between 34 and 45. Therefore, the integers in this range are:
\[ x = 35, 36, 37, 38, 39, 40, 41, 42, 43, 44 \]

- Cardinality \( n(T) = 10 \).

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### 7. \( W = \{x \mid 43 > x > 39\} \)

The values of \(x\) must be between 39 and 43. The integers in this range are:
\[ x = 40, 41, 42 \]

- Cardinality \( n(W) = 3 \).

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### 8. \( O = \{x \mid x \text{ is a negative integer greater than } -16\} \)

The negative integers greater than -16 are:
\[ x = -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1 \]

- Cardinality \( n(O) = 15 \).

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### 9. \( S = \{x \mid x \text{ is a whole number less than 19}\} \)

Whole numbers (non-negative integers) less than 19 are:
\[ x = 0, 1, 2, \dots, 18 \]

- Cardinality \( n(S) = 19 \).

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### 10. \( N = \{x \mid x \text{ is a positive integer less than 22}\} \)

The positive integers less than 22 are:
\[ x = 1, 2, 3, \dots, 21 \]

- Cardinality \( n(N) = 21 \).

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### Summary of Cardinalities:
- \( n(T) = 10 \)
- \( n(W) = 3 \)
- \( n(O) = 15 \)
- \( n(S) = 19 \)
- \( n(N) = 21 \)

Let me know if you want any additional details or have further questions!

### Related Questions:
1. What is the general method for determining the cardinality of a set?
2. How can the concept of cardinality be applied to infinite sets?
3. Can a set with repeating elements have a different cardinality from a set with distinct elements?
4. What is the cardinality of a set containing no elements (an empty set)?
5. How would the cardinality change if some of these sets allowed real numbers instead of integers?

#### Tip: 
When determining the cardinality of a set, always consider if the elements are distinct and whether any specific conditions (like being whole, negative, or positive) apply.

Identify the cardinality of the sets T, W, O, S, and N based on their set definitions.

Explore how to calculate the cardinality of sets based on integer ranges. This problem involves determining the number of distinct elements in sets T, W, O, S, and N. Key concepts include set theory and cardinality, suitable for students in Grades 6-8.

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