given the following sets, determine AGiven the following​ sets, determine A∩C  U={0,1,2,3,4,5,...} {A=1,2,3,4,...} C={2,4,6,8,...}


Let's find the intersection \(A \cap C\) of the given sets \(A\) and \(C\).

### Given Sets:
- **Universal Set \(U\)**: \(U = \{0, 1, 2, 3, 4, 5, \ldots\}\)  
  (This set includes all non-negative integers.)

- **Set \(A\)**: \(A = \{1, 2, 3, 4, \ldots\}\)  
  (This set includes all positive integers, which are natural numbers.)

- **Set \(C\)**: \(C = \{2, 4, 6, 8, \ldots\}\)  
  (This set includes all even positive integers.)

### Intersection of Sets \(A\) and \(C\):

The intersection \(A \cap C\) consists of all elements that are in both sets \(A\) and \(C\).

- **Set \(A\)** contains all positive integers: \(1, 2, 3, 4, 5, \ldots\).
- **Set \(C\)** contains all even positive integers: \(2, 4, 6, 8, \ldots\).

To find \(A \cap C\), we look for elements that are both in set \(A\) and set \(C\).

### Calculation of \(A \cap C\):

Since \(A\) contains all positive integers and \(C\) contains all even positive integers, the intersection \(A \cap C\) will be all the even positive integers that are in both \(A\) and \(C\).

\[
A \cap C = \{2, 4, 6, 8, 10, \ldots\}
\]

### Conclusion:

The intersection \(A \cap C\) is the set of all even positive integers:

\[
A \cap C = \{2, 4, 6, 8, 10, \ldots\}
\]

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. Determine the union \(A \cup C\) given the sets \(A = \{1, 2, 3, 4, \ldots\}\) and \(C = \{2, 4, 6, 8, \ldots\}\).
2. Find the set difference \(A - C\) for the sets \(A\) and \(C\).
3. What is the intersection \(B \cap C\) if \(B = \{1, 3, 5, 7, 9, \ldots\}\) and \(C = \{2, 4, 6, 8, \ldots\}\)?
4. If \(D = \{1, 2, 3, 5, 7, 9, \ldots\}\), what is \(D \cap C\)?
5. Determine the complement of \(C\) with respect to \(U\).

**Tip:** When finding the intersection of two sets, look for elements that appear in both sets.

Explore how to determine the intersection of sets A and C in set theory. Set A includes all positive integers, and set C consists of all even positive integers. Learn the method to find the intersection and apply it to similar problems. Suitable for Grades 9-12.

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