Question

let a be the set of numbers greater than 0 and less than 10 let b be the set of even numbers greater than 0 and less than 10 define both sets A= and B= AUC

Answer 1

Let's define the sets based on your description:

1. **Set A**: Set of numbers greater than 0 and less than 10.
\[
A = \{ x \in \mathbb{R} \mid 0 < x < 10 \}
\]
In terms of whole numbers (integers), this can be represented as:
\[
A = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9 \}
\]

2. **Set B**: Set of even numbers greater than 0 and less than 10.
\[
B = \{ x \in \mathbb{N} \mid x \text{ is even} \text{ and } 0 < x < 10 \}
\]
In terms of whole numbers (integers), this can be represented as:
\[
B = \{ 2, 4, 6, 8 \}
\]

3. **Union of Sets A and B (A ∪ B)**: This set consists of all elements that are in either set A or set B (or in both).
\[
A \cup B = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9 \} \cup \{ 2, 4, 6, 8 \} = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9 \}
\]

Since all even numbers in set B are already included in set A, the union does not add any new elements. Therefore:
\[
A \cup B = A = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9 \}
\]

In summary:
- Set A: \( \{ 1, 2, 3, 4, 5, 6, 7, 8, 9 \} \)
- Set B: \( \{ 2, 4, 6, 8 \} \)
- \( A \cup B = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9 \} \)