Which of the following statements is logically consistent with the definition of

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Question: Which of the following statements is logically consistent with the definition of multiples?

Options:

Correct Answer: The sum of two multiples of 3 is always a multiple of 3.

Solution:

The sum of two multiples of 3 is always a multiple of 3, as multiples of a number are closed under addition.

Which of the following statements is logically consistent with the definition of multiples?

Which of the following statements is logically consistent with the definition of multiples?

Step 1: Understand what a multiple is. A multiple of a number is the result of multiplying that number by an integer. For example, multiples of 3 are 3, 6, 9, 12, etc.
Step 2: Identify what it means for a number to be closed under addition. This means that if you take two numbers from a certain set (like multiples of 3) and add them together, the result will also be in that set.
Step 3: Take two multiples of 3. For example, let's take 3 (which is 3 x 1) and 6 (which is 3 x 2).
Step 4: Add these two multiples together. 3 + 6 = 9.
Step 5: Check if the result (9) is a multiple of 3. Since 9 can be expressed as 3 x 3, it is indeed a multiple of 3.
Step 6: Conclude that the sum of any two multiples of 3 will always be a multiple of 3, confirming that multiples of a number are closed under addition.

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