Let's define the sets based on your description:
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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: \[ A = { 1, 2, 3, 4, 5, 6, 7, 8, 9 } \]
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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: \[ B = { 2, 4, 6, 8 } \]
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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: \( { 2, 4, 6, 8 } \)
- \( A \cup B = { 1, 2, 3, 4, 5, 6, 7, 8, 9 } \)