https://r2.erweima.ai/mathbot/image/1726965502039sqc9meuh.jpg

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### Problem 1:
We are asked to determine the number of elements in the finite sets from problems 1 to 20. If the set is infinite, we write \( \infty \).

To solve:
- We would need the specific sets from exercises 1.6 (not provided in the image).
  
**Steps:**
- Identify each set in the given problems.
- Count the elements for finite sets.
- If a set is infinite, denote it as \( \infty \).

### Problem 4:
"A set with cardinality 3."
- A set with 3 elements can be: 
  \[
  \{1, 2, 3\}
  \]

### Problem 5:
"A set with cardinality 1."
- A set with 1 element can be:
  \[
  \{1\}
  \]

### Problem 6:
"A set with cardinality 0."
- A set with 0 elements is the empty set:
  \[
  \emptyset
  \]

### Problem 7:
"A set with cardinality 10."
- A set with 10 elements can be:
  \[
  \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}
  \]

### Problem 8:
"An infinite set."
- An example of an infinite set is the set of natural numbers:
  \[
  \mathbb{N} = \{1, 2, 3, 4, 5, 6, \dots\}
  \]

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Learn how to solve set theory problems involving cardinality, subsets, proper subsets, disjoint sets, and infinite sets. This includes counting elements of sets, identifying empty sets, and determining relations between sets. Suitable for high school and early university students.

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