If A = {x | x is an even integer} and B = {x | x is a multiple of 3}, what is A ∪ B?
Correct Answer: {0, 2, 3, 4, 6, 9, ...}
- Step 1: Understand what set A is. Set A includes all even integers, which are numbers like -4, -2, 0, 2, 4, 6, 8, and so on.
- Step 2: Understand what set B is. Set B includes all multiples of 3, which are numbers like -6, -3, 0, 3, 6, 9, 12, and so on.
- Step 3: Find the union of sets A and B, denoted as A ∪ B. The union means we combine all the elements from both sets without repeating any elements.
- Step 4: List some elements from set A: {0, 2, 4, 6, 8, ...}.
- Step 5: List some elements from set B: {0, 3, 6, 9, 12, ...}.
- Step 6: Combine the two lists, making sure not to repeat any numbers. The combined list will include all even integers and all multiples of 3.
- Step 7: Write the final result for A ∪ B, which includes numbers like {0, 2, 3, 4, 6, 8, 9, 12, ...}.
- Set Theory – Understanding the union of sets and how to combine elements from different sets.
- Even Integers – Recognizing the definition and properties of even integers.
- Multiples of 3 – Identifying multiples of 3 and their characteristics.
