Question 1. A group G is called divisible if it satisfies the following two properties: (1) G is an Abelian group, and (2) Given € G and a non-zero integer n, there exists a y = G such that y" = x. Notice that if the operation in your group is addition, y¹ = x means ny = x. (a) Prove that Q and R are divisible groups under addition. (b) Prove that Z under addition is not a divisible group. (c) Prove that the set of the positive rational numbers under multiplication is not a divisible group.

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