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 $n(T) = 10$.

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 $n(W) = 3$.

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 $n(O) = 15$.

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 $n(S) = 19$.

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 $n(N) = 21$.

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.