If A = {x | x is an even number} and B = {x | x is a multiple of 3}, what is A ∪ B?

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Q: If A = {x | x is an even number} and B = {x | x is a multiple of 3}, what is A ∪ B?

Solution: The union A ∪ B includes all even numbers and all multiples of 3. Thus, A ∪ B = {0, 2, 3, 4, 6, 9, ...}.

Steps: 7

Step 1: Understand what set A is. A = {x | x is an even number} means A includes all even numbers like 0, 2, 4, 6, 8, 10, ...
Step 2: Understand what set B is. B = {x | x is a multiple of 3} means B includes all multiples of 3 like 0, 3, 6, 9, 12, ...
Step 3: Find the union of sets A and B, denoted as A ∪ B. The union includes all elements from both sets without duplicates.
Step 4: List the elements from A: 0, 2, 4, 6, 8, 10, ...
Step 5: List the elements from B: 0, 3, 6, 9, 12, ...
Step 6: Combine the two lists, making sure to include each number only once. This gives us: 0, 2, 3, 4, 6, 8, 9, 10, 12, ...
Step 7: Write the final answer for A ∪ B, which includes all even numbers and all multiples of 3.