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This is a set theory question regarding relative complement.

If $A = \{n \in \Bbb{N} : 5 \mid n\}$ and $B = \{n \in \Bbb{N} : 10 \mid n\}$. List all of the elements that are in $A \setminus B$.

Wouldn't this be asking to list an infinite number of multiples of $5$ that have the multiples of $10$ taken away from them? If not, then what is this question expecting an answer of?

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    The question isn't very well phrased. By "listing" the elements I assume it means writing them as a set.2012-10-05

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Your answer is exactly right. You could write this set as $ A \setminus B = \{5, 15, 25, 35, \dots\} $ or more succinctly as $ A \setminus B = \{10m + 5 \mid m \in \mathbb{N}\}. $

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    Thank you very much. Same to everyone else. ^^2012-09-09
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The question is probably asking for a description of $A - B$. It is exactly as you said : it is the list of multiple of 5 with the multiple of 10 remove. In other word,

$A - B = \{5(2k + 1) : k \in \mathbb{N}\}$.

They are the numbers of the form $5$ times an odd number. (Note that 5 times an even number is always divisible by 10.)