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## Main Question or Discussion Point

I'm having a bit of a tough time interpreting <S> for a set S. I know for an element a, <a> is the set of all integral powers of a with respect to a given operation, but for a set S = {a, b, c}, what would <a, b, c> turn out as?

Edit: The source of my trouble is with this: The subgroup <9, 12> of the group of integers with addition as the operation contains 12 + (-9) = 3 (in order for it to be a group). Here is what the text says: "Therefore <9, 12> must contain all multiples of 3." I thought <9, 12> would only consist of multiples of 9 and 12, but apparently, there is more to it.

Edit: The source of my trouble is with this: The subgroup <9, 12> of the group of integers with addition as the operation contains 12 + (-9) = 3 (in order for it to be a group). Here is what the text says: "Therefore <9, 12> must contain all multiples of 3." I thought <9, 12> would only consist of multiples of 9 and 12, but apparently, there is more to it.

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