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

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

Options:

Correct Answer: {0, 2, 3, 4, 6, 9, ...}

Solution:

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

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

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.