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What meaning of the statement this: subgroups partition groups into subsets of equal size?

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Answer:

This statement means that subgroups divide a larger group into smaller groups, and each of these smaller groups has the same number of things in it. For example, if there are 12 people in a group, and they form subgroups of 3 people each in a group, there will be 4 groups total, and each individual subgroup will have 3 people in it.

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