If A = {x | x is a multiple of 3} and B = {x | x is a multiple of 5}, what is A

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Question: If A = {x | x is a multiple of 3} and B = {x | x is a multiple of 5}, what is A ∩ B?

Options:

Correct Answer: {0}

Solution:

The intersection A ∩ B consists of common multiples, which is {0}.

If A = {x | x is a multiple of 3} and B = {x | x is a multiple of 5}, what is A ∩ B?

If A = {x | x is a multiple of 3} and B = {x | x is a multiple of 5}, what is A ∩ B?

Step 1: Understand what set A is. A = {x | x is a multiple of 3} means A includes numbers like 0, 3, 6, 9, 12, etc.
Step 2: Understand what set B is. B = {x | x is a multiple of 5} means B includes numbers like 0, 5, 10, 15, 20, etc.
Step 3: Find the intersection A ∩ B. This means we need to find numbers that are in both set A and set B.
Step 4: Look for common multiples of 3 and 5. The first common multiple is 0, since 0 is a multiple of every number.
Step 5: Check if there are any other common multiples. The next common multiple of 3 and 5 is 15, but we are only looking for the intersection, which is the set of common multiples.
Step 6: Conclude that the only common multiple we found is 0, so A ∩ B = {0}.

Set Theory – Understanding the definition of sets, particularly the intersection of two sets.
Multiples – Identifying common multiples of given numbers (in this case, 3 and 5).